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Question 1:

Factorize each of the following expressions:
qr − pr + qs − ps

Question 2:

Factorize each of the following expressions:
p2qpr2 − pq + r2

Question 3:

Factorize each of the following expressions:
1 + x + xy + x2y

Question 4:

Factorize each of the following expressions:
ax + ay − bx − by

Question 5:

Factorize each of the following expressions:
xa2 + xb2ya2yb2

Question 6:

Factorize each of the following expressions:
x2 + xy + xz + yz

Question 7:

Factorize each of the following expressions:
2ax + bx + 2ay + by

Question 8:

Factorize each of the following expressions:
ab − by − ay + y2

Question 9:

Factorize each of the following expressions:
axy + bcxy − az − bcz

Question 10:

Factorize each of the following expressions:
lm2mn2lm + n2

Question 11:

Factorize each of the following expressions:
x3y2 + xx2y2

Question 12:

Factorize each of the following expressions:
6xy + 6 − 9y − 4x

Question 13:

Factorize each of the following expressions:
x2 − 2ax − 2ab + bx

Question 14:

Factorize each of the following expressions:
x3 − 2x2y + 3xy2 − 6y3

Question 15:

Factorize each of the following expression:
abx2 + (ay − b) x − y

Question 16:

Factorize each of the following expression:
(ax + by)2 + (bx − ay)2

Question 17:

Factorize each of the following expression:
16(a − b)3 − 24 (a − b)2

Question 18:

Factorize each of the following expression:
ab(x2 + 1) + x(a2 + b2)

Question 19:

Factorize each of the following expression:
a2x2 + (ax2 + 1)x + a

Question 20:

Factorize each of the following expression:
a(a − 2bc) + 2bc

Question 21:

Factorize each of the following expression:
a(a + b − c) − bc

Question 22:

Factorize each of the following expression:
x2 − 11xyx + 11y

Question 23:

Factorize each of the following expression:
ab − a − b + 1

Question 24:

Factorize each of the following expression:
x2 + y − xy − x

Question 1:

Factorize each of the following expression:
16x2 − 25y2

$16{x}^{2}-25{y}^{2}\phantom{\rule{0ex}{0ex}}=\left(4x{\right)}^{2}-\left(5y{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(4x-5y\right)\left(4x+5y\right)$

Question 2:

Factorize each of the following expression:
27x2 − 12y2

$27{x}^{2}-12{y}^{2}\phantom{\rule{0ex}{0ex}}=3\left(9{x}^{2}-4{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=3\left[\left(3x{\right)}^{2}-\left(2y{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=3\left(3x-2y\right)\left(3x+2y\right)$

Question 3:

Factorize each of the following expression:
144a2 − 289b2

$144{a}^{2}-289{b}^{2}\phantom{\rule{0ex}{0ex}}=\left(12a{\right)}^{2}-\left(17b{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(12a-17b\right)\left(12a+17b\right)$

Question 4:

Factorize each of the following expression:
12m2 − 27

$12{m}^{2}-27\phantom{\rule{0ex}{0ex}}=3\left(4{m}^{2}-9\right)\phantom{\rule{0ex}{0ex}}=3\left[\left(2m{\right)}^{2}-{3}^{2}\right]\phantom{\rule{0ex}{0ex}}=3\left(2m-3\right)\left(2m+3\right)$

Question 5:

Factorize each of the following expression:
125x2 − 45y2

$125{x}^{2}-45{y}^{2}\phantom{\rule{0ex}{0ex}}=5\left(25{x}^{2}-9{y}^{2}\right)\phantom{\rule{0ex}{0ex}}=5\left[\left(5x{\right)}^{2}-\left(3y{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=5\left(5x-3y\right)\left(5x+3y\right)$

Question 6:

Factorize each of the following expression:
144a2 − 169b2

$144{a}^{2}-169{b}^{2}\phantom{\rule{0ex}{0ex}}=\left(12a{\right)}^{2}-\left(13b{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(12a-13b\right)\left(12a+13b\right)$

Question 7:

Factorize each of the following expression:
(2a − b)2 − 16c2

$\left(2a-b{\right)}^{2}-16{c}^{2}\phantom{\rule{0ex}{0ex}}=\left(2a-b{\right)}^{2}-\left(4c{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(2a-b\right)-4c\right]\left[\left(2a-b\right)+4c\right]\phantom{\rule{0ex}{0ex}}=\left(2a-b-4c\right)\left(2a-b+4c\right)$

Question 8:

Factorize each of the following expression:
(x + 2y)2 − 4(2x − y)2

Question 9:

Factorize each of the following expression:
3a5 − 48a3

$3{a}^{5}-48{a}^{3}\phantom{\rule{0ex}{0ex}}=3{a}^{3}\left({a}^{2}-16\right)\phantom{\rule{0ex}{0ex}}=3{a}^{3}\left({a}^{2}-{4}^{2}\right)\phantom{\rule{0ex}{0ex}}=3{a}^{3}\left(a-4\right)\left(a+4\right)$

Question 10:

Factorize each of the following expression:
a4 − 16b4

Question 11:

Factorize each of the following expression:
x8 − 1

${x}^{8}-1\phantom{\rule{0ex}{0ex}}=\left({x}^{4}{\right)}^{2}-{1}^{2}\phantom{\rule{0ex}{0ex}}=\left({x}^{4}-1\right)\left({x}^{4}+1\right)\phantom{\rule{0ex}{0ex}}=\left[\left({x}^{2}{\right)}^{2}-{1}^{2}\right]\left({x}^{4}+1\right)\phantom{\rule{0ex}{0ex}}=\left({x}^{2}-1\right)\left({x}^{2}+1\right)\left({x}^{4}+1\right)\phantom{\rule{0ex}{0ex}}=\left({x}^{2}-{1}^{2}\right)\left({x}^{2}+1\right)\left({x}^{4}+1\right)\phantom{\rule{0ex}{0ex}}=\left(x-1\right)\left(x+1\right)\left({x}^{2}+1\right)\left({x}^{4}+1\right)$

Question 12:

Factorize each of the following expression:
64 − (a + 1)2

$64-\left(a+1{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(8{\right)}^{2}-\left(a+1{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[8-\left(a+1\right)\right]\left[8+\left(a+1\right)\right]\phantom{\rule{0ex}{0ex}}=\left(8-a-1\right)\left(8+a+1\right)\phantom{\rule{0ex}{0ex}}=\left(7-a\right)\left(9+a\right)$

Question 13:

Factorize each of the following expression:
36l2 − (m + n)2

$36{l}^{2}-\left(m+n{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(6l{\right)}^{2}-\left(m+n{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[6l-\left(m+n\right)\right]\left[6l+\left(m+n\right)\right]\phantom{\rule{0ex}{0ex}}=\left(6l-m-n\right)\left(6l+m+n\right)$

Question 14:

Factorize each of the following expression:
25x4y4 − 1

$25{x}^{4}{y}^{4}-1\phantom{\rule{0ex}{0ex}}=\left(5{x}^{2}{y}^{2}{\right)}^{2}-1\phantom{\rule{0ex}{0ex}}=\left(5{x}^{2}{y}^{2}-1\right)\left(5{x}^{2}{y}^{2}+1\right)$

Question 15:

Factorize each of the following expression:
${a}^{4}-\frac{1}{{b}^{4}}$

1/b4
(a2)1/(b2)2
a2- 1/b2a2 1/b2
1/ba 1/ba2 1/b2

Question 16:

Factorize each of the following expression:
x3 − 144x

${x}^{3}-144x\phantom{\rule{0ex}{0ex}}=x\left({x}^{2}-144\right)\phantom{\rule{0ex}{0ex}}=x\left({x}^{2}-{12}^{2}\right)\phantom{\rule{0ex}{0ex}}=x\left(x-12\right)\left(x+12\right)$

Question 17:

Factorize each of the following expression:
(x - 4y)2 − 625

$\left(x-4y{\right)}^{2}-625\phantom{\rule{0ex}{0ex}}=\left(x-4y{\right)}^{2}-{25}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(x-4y\right)-25\right]\left[\left(x-4y\right)+25\right]\phantom{\rule{0ex}{0ex}}=\left(x-4y-25\right)\left(x-4y+25\right)$

Question 18:

Factorize each of the following expression:
9(a − b)2 − 100(x − y)2

$9\left(a-b{\right)}^{2}-100\left(x-y{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[3\left(a-b\right){\right]}^{2}-\left[10\left(x-y\right){\right]}^{2}\phantom{\rule{0ex}{0ex}}=\left[3\left(a-b\right)-10\left(x-y\right)\right]\left[3\left(a-b\right)+10\left(x-y\right)\right]\phantom{\rule{0ex}{0ex}}=\left(3a-3b-10x+10y\right)\left(3a-3b+10x-10y\right)$

Question 19:

Factorize each of the following expression:
(3 + 2a)2 − 25a2

$\left(3+2a{\right)}^{2}-25{a}^{2}\phantom{\rule{0ex}{0ex}}=\left(3+2a{\right)}^{2}-\left(5a{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(3+2a\right)-5a\right]\left[\left(3+2a\right)+5a\right]\phantom{\rule{0ex}{0ex}}=\left(3+2a-5a\right)\left(3+2a+5a\right)\phantom{\rule{0ex}{0ex}}=\left(3-3a\right)\left(3+7a\right)\phantom{\rule{0ex}{0ex}}=3\left(1-a\right)\left(3+7a\right)$

Question 20:

Factorize each of the following expression:
(x + y)2 − (a − b)2

$\left(x+y{\right)}^{2}-\left(a-b{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(x+y\right)-\left(a-b\right)\right]\left[\left(x+y\right)+\left(a-b\right)\right]\phantom{\rule{0ex}{0ex}}=\left(x+y-a+b\right)\left(x+y+a-b\right)$

Question 21:

Factorize each of the following expression:
$\frac{1}{16}{x}^{2}{y}^{2}-\frac{4}{49}{y}^{2}{z}^{2}$

$\frac{1}{16}{x}^{2}{y}^{2}-\frac{4}{49}{y}^{2}{z}^{2}\phantom{\rule{0ex}{0ex}}={y}^{2}\left(\frac{1}{16}{x}^{2}-\frac{4}{49}{z}^{2}\right)\phantom{\rule{0ex}{0ex}}={y}^{2}\left[{\left(\frac{1}{4}x\right)}^{2}-{\left(\frac{2}{7}z\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}={y}^{2}\left(\frac{1}{4}x-\frac{2}{7}z\right)\left(\frac{1}{4}x+\frac{2}{7}z\right)\phantom{\rule{0ex}{0ex}}={y}^{2}\left(\frac{x}{4}-\frac{2}{7}z\right)\left(\frac{x}{4}+\frac{2}{7}z\right)$

Question 22:

Factorize each of the following expression:
75a3b2 - 108ab4

$75{a}^{3}{b}^{2}-108a{b}^{4}\phantom{\rule{0ex}{0ex}}=3a{b}^{2}\left(25{a}^{2}-36{b}^{2}\right)\phantom{\rule{0ex}{0ex}}=3a{b}^{2}\left[\left(5a{\right)}^{2}-\left(6b{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=3a{b}^{2}\left(5a-6b\right)\left(5a+6b\right)$

Question 23:

Factorize each of the following expression:
x5 − 16x3

${x}^{5}-16{x}^{3}\phantom{\rule{0ex}{0ex}}={x}^{3}\left({x}^{2}-16\right)\phantom{\rule{0ex}{0ex}}={x}^{3}\left({x}^{2}-{4}^{2}\right)\phantom{\rule{0ex}{0ex}}={x}^{3}\left(x-4\right)\left(x+4\right)$

Question 24:

Factorize each of the following expression:
$\frac{50}{{x}^{2}}-\frac{2{x}^{2}}{81}$

Question 25:

Factorize each of the following expression:
256x5 − 81x

$256{x}^{5}-81x\phantom{\rule{0ex}{0ex}}=x\left(256{x}^{4}-81\right)\phantom{\rule{0ex}{0ex}}=x\left[\left(16{x}^{2}{\right)}^{2}-{9}^{2}\right]\phantom{\rule{0ex}{0ex}}=x\left(16{x}^{2}+9\right)\left(16{x}^{2}-9\right)\phantom{\rule{0ex}{0ex}}=x\left(16{x}^{2}+9\right)\left[\left(4x{\right)}^{2}-{3}^{2}\right]\phantom{\rule{0ex}{0ex}}=x\left(16{x}^{2}+9\right)\left(4x+3\right)\left(4x-3\right)$

Question 26:

Factorize each of the following expression:
a4 − (2b + c)4

${a}^{4}-\left(2b+c{\right)}^{4}\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{\right)}^{2}-\left[\left(2b+c{\right)}^{2}{\right]}^{2}\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+\left(2b+c{\right)}^{2}\right]\left[{a}^{2}-\left(2b+c{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+\left(2b+c{\right)}^{2}\right]\left\{\left[a+\left(2b+c\right)\right]\left[a-\left(2b+c\right)\right]\right\}\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+\left(2b+c{\right)}^{2}\right]\left(a+2b+c\right)\left(a-2b-c\right)$

Question 27:

Factorize each of the following expression:
(3x + 4y)4x4

$\left(3\mathrm{x}+4\mathrm{y}{\right)}^{4}-{\mathrm{x}}^{4}\phantom{\rule{0ex}{0ex}}=\left[\left(3\mathrm{x}+4\mathrm{y}{\right)}^{2}{\right]}^{2}-\left({\mathrm{x}}^{2}{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(3\mathrm{x}+4\mathrm{y}{\right)}^{2}+{\mathrm{x}}^{2}\right]\left[\left(3\mathrm{x}+4\mathrm{y}{\right)}^{2}-{\mathrm{x}}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left[\left(3\mathrm{x}+4\mathrm{y}{\right)}^{2}+{\mathrm{x}}^{2}\right]\left[\left(3\mathrm{x}+4\mathrm{y}\right)+\mathrm{x}\right]\left[\left(3\mathrm{x}+4\mathrm{y}\right)-\mathrm{x}\right]\phantom{\rule{0ex}{0ex}}=\left\{\left(3\mathrm{x}+4\mathrm{y}{\right)}^{2}+{\mathrm{x}}^{2}\right\}\left(3\mathrm{x}+4\mathrm{y}+\mathrm{x}\right)\left(3\mathrm{x}+4\mathrm{y}-\mathrm{x}\right)\phantom{\rule{0ex}{0ex}}=\left\{{\left(3\mathrm{x}+4\mathrm{y}\right)}^{2}+{\mathrm{x}}^{2}\right\}\left(4\mathrm{x}+4\mathrm{y}\right)\left(2\mathrm{x}+4\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=\left\{{\left(3\mathrm{x}+4\mathrm{y}\right)}^{2}+{\mathrm{x}}^{2}\right\}4\left(\mathrm{x}+\mathrm{y}\right)2\left(\mathrm{x}+2\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=8\left\{{\left(3\mathrm{x}+4\mathrm{y}\right)}^{2}+{\mathrm{x}}^{2}\right\}\left(\mathrm{x}+\mathrm{y}\right)\left(\mathrm{x}+2\mathrm{y}\right)$

Question 28:

Factorize each of the following expression:
p2q2p4q4

${p}^{2}{q}^{2}-{p}^{4}{q}^{4}\phantom{\rule{0ex}{0ex}}={p}^{2}{q}^{2}\left(1-{p}^{2}{q}^{2}\right)\phantom{\rule{0ex}{0ex}}={p}^{2}{q}^{2}\left[1-\left(pq{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}={p}^{2}{q}^{2}\left(1-pq\right)\left(1+pq\right)$

Question 29:

Factorize each of the following expression:
3x3y − 243xy3

Question 30:

Factorize each of the following expression:
a4b4 − 16c4

${a}^{4}{b}^{4}-16{c}^{4}\phantom{\rule{0ex}{0ex}}=\left[\left({a}^{2}{b}^{2}{\right)}^{2}-\left(4{c}^{2}{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+4{c}^{2}\right)\left({a}^{2}{b}^{2}-4{c}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+4{c}^{2}\right)\left[\left(ab{\right)}^{2}-\left(2c{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+4{c}^{2}\right)\left(ab+2c\right)\left(ab-2c\right)$

Question 31:

Factorize each of the following expression:
x4 − 625

${x}^{4}-625\phantom{\rule{0ex}{0ex}}=\left({x}^{2}{\right)}^{2}-{25}^{2}\phantom{\rule{0ex}{0ex}}=\left({x}^{2}+25\right)\left({x}^{2}-25\right)\phantom{\rule{0ex}{0ex}}=\left({x}^{2}+25\right)\left({x}^{2}-{5}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left({x}^{2}+25\right)\left(x+5\right)\left(x-5\right)$

Question 32:

Factorize each of the following expression:
x4 − 1

Question 33:

Factorize each of the following expression:
49(a − b)2 − 25(a + b)2

$49\left(a-b{\right)}^{2}-25\left(a+b{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[7\left(a-b\right){\right]}^{2}-\left[5\left(a+b\right){\right]}^{2}\phantom{\rule{0ex}{0ex}}=\left[7\left(a-b\right)-5\left(a+b\right)\right]\left[7\left(a-b\right)+5\left(a+b\right)\right]\phantom{\rule{0ex}{0ex}}=\left(7a-7b-5a-5b\right)\left(7a-7b+5a+5b\right)\phantom{\rule{0ex}{0ex}}=\left(2a-12b\right)\left(12a-2b\right)\phantom{\rule{0ex}{0ex}}=2\left(a-6b\right)2\left(6a-b\right)\phantom{\rule{0ex}{0ex}}=4\left(a-6b\right)\left(6a-b\right)$

Question 34:

Factorize each of the following expression:
x − yx2 + y2

Question 35:

Factorize each of the following expression:
16(2x − 1)2 − 25y2

$16\left(2x-1{\right)}^{2}-25{y}^{2}\phantom{\rule{0ex}{0ex}}=\left[4\left(2x-1\right){\right]}^{2}-\left(5y{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[4\left(2x-1\right)-5y\right]\left[4\left(2x-1\right)+5y\right]\phantom{\rule{0ex}{0ex}}=\left(8x-4-5y\right)\left(8x-4+5y\right)\phantom{\rule{0ex}{0ex}}=\left(8x-5y-4\right)\left(8x+5y-4\right)$

Question 36:

Factorize each of the following expression:
4(xy + 1)2 − 9(x − 1)2

$4\left(xy+1{\right)}^{2}-9\left(x-1{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[2\left(xy+1\right){\right]}^{2}-\left[3\left(x-1\right){\right]}^{2}\phantom{\rule{0ex}{0ex}}=\left[2\left(xy+1\right)-3\left(x-1\right)\right]\left[2\left(xy+1\right)+3\left(x-1\right)\right]\phantom{\rule{0ex}{0ex}}=\left(2xy+2-3x+3\right)\left(2xy+2+3x-3\right)\phantom{\rule{0ex}{0ex}}=\left(2xy-3x+5\right)\left(2xy+3x-1\right)$

Question 37:

Factorize each of the following expression:
(2x + 1)2 − 9x4

Question 38:

Factorize each of the following expression:
x4 − (2y − 3z)2

Question 39:

Factorize each of the following expression:
a2b2 + a − b

Question 40:

Factorize each of the following expression:
16a4b4

$16{a}^{4}-{b}^{4}\phantom{\rule{0ex}{0ex}}=\left(4{a}^{2}{\right)}^{2}-\left({b}^{2}{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left(4{a}^{2}+{b}^{2}\right)\left(4{a}^{2}-{b}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(4{a}^{2}+{b}^{2}\right)\left[\left(2a{\right)}^{2}-{b}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left(4{a}^{2}+{b}^{2}\right)\left(2a+b\right)\left(2a-b\right)$

Question 41:

Factorize each of the following expression:
a4 − 16(b − c)4

${a}^{4}-16\left(b-c{\right)}^{4}\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{\right)}^{2}-\left[4\left(b-c{\right)}^{2}{\right]}^{2}\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+4\left(b-c{\right)}^{2}\right]\left[{a}^{2}-4\left(b-c{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+4\left(b-c{\right)}^{2}\right]\left\{{a}^{2}-\left[2\left(b-c\right){\right]}^{2}\right\}\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+4\left(b-c{\right)}^{2}\right]\left[a+2\left(b-c\right)\right]\left[a-2\left(b-c\right)\right]\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}+4\left(b-c{\right)}^{2}\right]\left(a+2b-2c\right)\left(a-2b+2c\right)$

Question 42:

Factorize each of the following expression:
2a5 − 32a

$2{a}^{5}-32a\phantom{\rule{0ex}{0ex}}=2a\left({a}^{4}-16\right)\phantom{\rule{0ex}{0ex}}=2a\left[\left({a}^{2}{\right)}^{2}-{4}^{2}\right]\phantom{\rule{0ex}{0ex}}=2a\left({a}^{2}+4\right)\left({a}^{2}-4\right)\phantom{\rule{0ex}{0ex}}=2a\left({a}^{2}+4\right)\left({a}^{2}-{2}^{2}\right)\phantom{\rule{0ex}{0ex}}=2a\left({a}^{2}+4\right)\left(a+2\right)\left(a-2\right)\phantom{\rule{0ex}{0ex}}=2a\left(a-2\right)\left(a+2\right)\left({a}^{2}+4\right)$

Question 43:

Factorize each of the following expression:
a4b4 − 81c4

${a}^{4}{b}^{4}-81{c}^{4}\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}{\right)}^{2}-\left(9{c}^{2}{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+9{c}^{2}\right)\left({a}^{2}{b}^{2}-9{c}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+9{c}^{2}\right)\left[\left(ab{\right)}^{2}-\left(3c{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=\left({a}^{2}{b}^{2}+9{c}^{2}\right)\left(ab+3c\right)\left(ab-3c\right)$

Question 44:

Factorize each of the following expression:
xy9yx9

$x{y}^{9}-y{x}^{9}\phantom{\rule{0ex}{0ex}}=xy\left({y}^{8}-{x}^{8}\right)\phantom{\rule{0ex}{0ex}}=xy\left[\left({y}^{4}{\right)}^{2}-\left({x}^{4}{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=xy\left({y}^{4}+{x}^{4}\right)\left({y}^{4}-{x}^{4}\right)\phantom{\rule{0ex}{0ex}}=xy\left({y}^{4}+{x}^{4}\right)\left[\left({y}^{2}{\right)}^{2}-\left({x}^{2}{\right)}^{2}\right]\phantom{\rule{0ex}{0ex}}=xy\left({y}^{4}+{x}^{4}\right)\left({y}^{2}+{x}^{2}\right)\left({y}^{2}-{x}^{2}\right)\phantom{\rule{0ex}{0ex}}=xy\left({y}^{4}+{x}^{4}\right)\left({y}^{2}+{x}^{2}\right)\left(y+x\right)\left(y-x\right)$

Question 45:

Factorize each of the following expression:
x3x

${x}^{3}-x\phantom{\rule{0ex}{0ex}}=x\left({x}^{2}-1\right)\phantom{\rule{0ex}{0ex}}=x\left(x-1\right)\left(x+1\right)$

Question 46:

Factorize each of the following expression:
18a2x2 − 32

Question 1:

Factorize each of the following algebraic expression:
4x2 + 12xy +9y2

Question 2:

Factorize each of the following algebraic expression:
9a2 − 24ab + 16b2

Question 3:

Factorize each of the following algebraic expression:
p2q2 − 6pqr + 9r2

Question 4:

Factorize each of the following algebraic expression:
36a2 + 36a + 9

$36{\mathrm{a}}^{2}+36\mathrm{a}+9\phantom{\rule{0ex}{0ex}}=9\left(4{\mathrm{a}}^{2}+4\mathrm{a}+1\right)\phantom{\rule{0ex}{0ex}}=9\left\{\left(2\mathrm{a}{\right)}^{2}+2×2\mathrm{a}×1+{1}^{2}\right\}\phantom{\rule{0ex}{0ex}}=9\left(2\mathrm{a}+1{\right)}^{2}\phantom{\rule{0ex}{0ex}}=9\left(2\mathrm{a}+1\right)\left(2\mathrm{a}+1\right)$

Question 5:

Factorize each of the following algebraic expression:
a2 + 2ab + b2 − 16

Question 6:

Factorize each of the following algebraic expression:
9z2x2 + 4xy − 4y2

Question 7:

Factorize each of the following algebraic expression:
9a4 − 24a2b2 + 16b4 − 256

Question 8:

Factorize each of the following algebraic expression:
16 − a6 + 4a3b3 − 4b6

Question 9:

Factorize each of the following algebraic expression:
a2 − 2ab + b2c2

Question 10:

Factorize each of the following algebraic expression:
x2 + 2x + 1 − 9y2

Question 11:

Factorize each of the following algebraic expression:
a2 + 4ab + 3b2

Question 12:

Factorize each of the following algebraic expression:
96 − 4xx2

Question 13:

Factorize each of the following algebraic expression:
a4 + 3a2 +4

Question 14:

Factorize each of the following algebraic expression:
4x4 + 1

Question 15:

Factorize each of the following algebraic expression:
4x4 + y4

Question 16:

Factorize each of the following algebraic expression:
(x + 2)2 − 6(x + 2) + 9

Question 17:

Factorize each of the following algebraic expression:
25 − p2q2 − 2pq

Question 18:

Factorize each of the following algebraic expression:
x2 + 9y2 − 6xy − 25a2

Question 19:

Factorize each of the following algebraic expression:
49 − a2 + 8ab − 16b2

Question 20:

Factorize each of the following algebraic expression:
a2 − 8ab + 16b2 − 25c2

Question 21:

Factorize each of the following algebraic expression:
x2y2 + 6y − 9

${x}^{2}-{y}^{2}+6y-9\phantom{\rule{0ex}{0ex}}={x}^{2}-\left({y}^{2}-6y+9\right)\phantom{\rule{0ex}{0ex}}={x}^{2}-\left({y}^{2}-2×y×3+{3}^{2}\right)\phantom{\rule{0ex}{0ex}}={x}^{2}-\left(y-3{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[x-\left(y-3\right)\right]\left[x+\left(y-3\right)\right]\phantom{\rule{0ex}{0ex}}=\left(x-y+3\right)\left(x+y-3\right)$

Question 22:

Factorize each of the following algebraic expression:
25x2 − 10x + 1 − 36y2

$25{x}^{2}-10x+1-36{y}^{2}\phantom{\rule{0ex}{0ex}}=\left(25{x}^{2}-10x+1\right)-36{y}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(5x{\right)}^{2}-2×5x×1+1\right]-36{y}^{2}\phantom{\rule{0ex}{0ex}}=\left(5x-1{\right)}^{2}-\left(6y{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(5x-1\right)-6y\right]\left[\left(5x-1\right)+6y\right]\phantom{\rule{0ex}{0ex}}=\left(5x-1-6y\right)\left(5x-1+6y\right)\phantom{\rule{0ex}{0ex}}=\left(5x-6y-1\right)\left(5x+6y-1\right)$

Question 23:

Factorize each of the following algebraic expression:
a2 b2 + 2bc c2

${a}^{2}-{b}^{2}+2bc-{c}^{2}\phantom{\rule{0ex}{0ex}}={a}^{2}-\left({b}^{2}-2bc+{c}^{2}\right)\phantom{\rule{0ex}{0ex}}={a}^{2}-\left({b}^{2}-2×b×c+{c}^{2}\right)\phantom{\rule{0ex}{0ex}}={a}^{2}-\left(b-c{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(a-\left(b-c\right)\right]\left[\left(a+\left(b-c\right)\right]\phantom{\rule{0ex}{0ex}}=\left(a-b+c\right)\left(a+b-c\right)$

Question 24:

Factorize each of the following algebraic expression:
a2 + 2ab + b2c2

Question 25:

Factorize each of the following algebraic expression:
49 − x2y2 + 2xy

$49-{\mathrm{x}}^{2}-{\mathrm{y}}^{2}+2\mathrm{xy}\phantom{\rule{0ex}{0ex}}=49-\left({\mathrm{x}}^{2}-2\mathrm{xy}+{\mathrm{y}}^{2}\right)\phantom{\rule{0ex}{0ex}}=49-\left({\mathrm{x}}^{2}-2×\mathrm{x}×\mathrm{y}+{\mathrm{y}}^{2}\right)\phantom{\rule{0ex}{0ex}}={7}^{2}-\left(\mathrm{x}-\mathrm{y}{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[7-\left(\mathrm{x}-\mathrm{y}\right)\right]\left[7+\left(\mathrm{x}-\mathrm{y}\right)\right]\phantom{\rule{0ex}{0ex}}=\left(7-\mathrm{x}+\mathrm{y}\right)\left(7+\mathrm{x}-\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=\left(\mathrm{x}-\mathrm{y}+7\right)\left(\mathrm{y}-\mathrm{x}+7\right)$

Question 26:

Factorize each of the following algebraic expression:
a2 + 4b2 − 4ab − 4c2

${a}^{2}+4{b}^{2}-4ab-4{c}^{2}\phantom{\rule{0ex}{0ex}}=\left({a}^{2}-4ab+4{b}^{2}\right)-4{c}^{2}\phantom{\rule{0ex}{0ex}}=\left[{a}^{2}-2×a×2b+\left(2b{\right)}^{2}\right]-4{c}^{2}\phantom{\rule{0ex}{0ex}}=\left(a-2b{\right)}^{2}-\left(2c{\right)}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(a-2b\right)-2c\right]\left[\left(a-2b\right)+2c\right]\phantom{\rule{0ex}{0ex}}=\left(a-2b-2c\right)\left(a-2b+2c\right)$

Question 27:

Factorize each of the following algebraic expression:
x2y2 − 4xz + 4z2

${\mathrm{x}}^{2}-{\mathrm{y}}^{2}-4\mathrm{xz}+4{\mathrm{z}}^{2}\phantom{\rule{0ex}{0ex}}=\left({\mathrm{x}}^{2}-4\mathrm{xz}+4{\mathrm{z}}^{2}\right)-{\mathrm{y}}^{2}\phantom{\rule{0ex}{0ex}}=\left[{\mathrm{x}}^{2}-2×\mathrm{x}×2\mathrm{z}+\left(2\mathrm{z}{\right)}^{2}\right]-{\mathrm{y}}^{2}\phantom{\rule{0ex}{0ex}}=\left(\mathrm{x}-2\mathrm{z}{\right)}^{2}-{\mathrm{y}}^{2}\phantom{\rule{0ex}{0ex}}=\left[\left(\mathrm{x}-2\mathrm{z}\right)-\mathrm{y}\right]\left[\left(\mathrm{x}-2\mathrm{z}\right)+\mathrm{y}\right]\phantom{\rule{0ex}{0ex}}=\left(\mathrm{x}-2\mathrm{z}-\mathrm{y}\right)\left(\mathrm{x}-2\mathrm{z}+\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=\left(\mathrm{x}+\mathrm{y}-2\mathrm{z}\right)\left(\mathrm{x}-\mathrm{y}-2\mathrm{z}\right)$

Question 1:

Factorize each of the following algebraic expression:
x2 + 12x − 45

Question 2:

Factorize each of the following algebraic expression:
40 + 3xx2

Question 3:

Factorize each of the following algebraic expression:
a2 + 3a − 88

Question 4:

Factorize each of the following algebraic expression:
a2 − 14a − 51

Question 5:

Factorize each of the following algebraic expression:
x2 + 14x + 45

Question 6:

Factorize each of the following algebraic expression:
x2 − 22x + 120

Question 7:

Factorize each of the following algebraic expression:
x2 − 11x − 42

Question 8:

Factorize each of the following algebraic expression:
a2 + 2a − 3

Question 9:

Factorize each of the following algebraic expression:
a2 + 14a + 48

Question 10:

Factorize each of the following algebraic expression:
x2 − 4x − 21

Question 11:

Factorize each of the following algebraic expression:
y2 + 5y − 36

Question 12:

Factorize each of the following algebraic expression:
(a2 − 5a)2 − 36

Question 13:

Factorize each of the following algebraic expression:
(a + 7)(a − 10) + 16

Question 1:

Resolve each of the following quadratic trinomial into factor:
2x2 + 5x + 3

Question 2:

Resolve each of the following quadratic trinomial into factor:
2x2 − 3x − 2

Question 3:

Resolve each of the following quadratic trinomial into factor:
3x2 + 10x + 3

Question 4:

Resolve each of the following quadratic trinomial into factor:
7x − 6 − 2x2

Question 5:

Resolve each of the following quadratic trinomial into factor:
7x2 − 19x − 6

Question 6:

Resolve each of the following quadratic trinomial into factor:
28 − 31x − 5x2

Question 7:

Resolve each of the following quadratic trinomial into factor:
3 + 23y − 8y2

Question 8:

Resolve each of the following quadratic trinomial into factor:
11x2 − 54x + 63

Question 9:

Resolve each of the following quadratic trinomial into factor:
7x − 6x2 + 20

Question 10:

Resolve each of the following quadratic trinomial into factor:
3x2 + 22x + 35

Question 11:

Resolve each of the following quadratic trinomial into factor:
12x2 − 17xy + 6y2

Question 12:

Resolve each of the following quadratic trinomial into factor:
6x2 − 5xy − 6y2

Question 13:

Resolve each of the following quadratic trinomial into factor:
6x2 − 13xy + 2y2

Question 14:

Resolve each of the following quadratic trinomial into factor:
14x2 + 11xy − 15y2

Question 15:

Resolve each of the following quadratic trinomial into factor:
6a2 + 17ab3b2

Question 16:

Resolve each of the following quadratic trinomial into factor:
36a2 + 12abc − 15b2c2

Question 17:

Resolve each of the following quadratic trinomial into factor:
15x2 − 16xyz − 15y2z2

Question 18:

Resolve each of the following quadratic trinomial into factor:
(x − 2y)2 − 5(x − 2y) + 6

Question 19:

Resolve each of the following quadratic trinomial into factor:
(2a − b)2 + 2(2a − b) − 8

Question 1:

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x2 and 12x2

The numerical coefficients of the given monomials are 2 and 12. So, the greatest common factor of 2 and 12 is 2.
The common literal appearing in the given monomials is x.
The smallest power of x in the two monomials is 2.
The monomial of the common literals with the smallest powers is x2.
Hence, the greatest common factor is 2x2.

Question 2:

Find the greatest common factor (GCF/HCF) of the following polynomial:
6x3y and 18x2y3

The numerical coefficients of the given monomials are 6 and 18. The greatest common factor of 6 and 18 is 6.
The common literals appearing in the two monomials are x and y.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The monomial of the common literals with the smallest powers is x2y.
â€‹Hence, the greatest common factor is 6x2yâ€‹.

Question 3:

Find the greatest common factor (GCF/HCF) of the following polynomial:
7x, 21x2 and 14xy2

The numerical coefficients of the given monomials are 7, 21 and 14. The greatest common factor of 7, 21 and 14 is 7.
The common literal appearing in the three monomials is x.
The smallest power of x in the three monomials is 1.
The monomial of the common literals with the smallest powers is x.
â€‹Hence, the greatest common factor is 7x.

Question 4:

Find the greatest common factor (GCF/HCF) of the following polynomial:
42x2yz and 63x3y2z3

The numerical coefficients of the given monomials are 42 and 63. The greatest common factor of 42 and 63 is 21.
The common literals appearing in the two monomials are x, y and z.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 1.
The smallest power of z in the two monomials is 1
.
The monomial of the common literals with the smallest powers is x2yz.
â€‹Hence, the greatest common factor is
21x2yzâ€‹.

Question 5:

Find the greatest common factor (GCF/HCF) of the following polynomial:
12ax2, 6a2x3 and 2a3x5

The numerical coefficients of the given monomials are 12, 6 and 2. The greatest common factor of 12, 6 and 2 is 2.
The common literals appearing in the three monomials are a and x.
The smallest power of a in the three monomials is 1.
The smallest power of x in the three monomials is 2
.
The monomial of common literals with the smallest powers is ax2.
â€‹Hence, the greatest common factor is
2ax2.

Question 6:

Find the greatest common factor (GCF/HCF) of the following polynomial:
9x2, 15x2y3, 6xy2 and 21x2y2

The numerical coefficients of the given monomials are 9, 15, 6 and 21. The greatest common factor of 9, 15, 6 and 21 is 3.
The common literal appearing in the three monomials is x.
The smallest power of x in the four monomials is 1.
The monomial of common literals with the smallest powers is x.
â€‹Hence, the greatest common factor is
3x.

Question 7:

Find the greatest common factor (GCF/HCF) of the following polynomial:
4a2b3, −12a3b, 18a4b3

The numerical coefficients of the given monomials are 4, -12 and 18. The greatest common factor of 4, -12 and 18 is 2.
The common literals appearing in the three monomials are a and b.
The smallest power of a in the three monomials is 2.
The smallest power of b in the three monomials is 1.

The monomial of the common literals with the smallest powers is a2b.
â€‹Hence, the greatest common factor is
2a2bâ€‹.

Question 8:

Find the greatest common factor (GCF/HCF) of the following polynomial:
6x2y2, 9xy3, 3x3y2

The numerical coefficients of the given monomials are 6, 9 and 3. The greatest common factor of 6, 9 and 3 is 3.
The common literals appearing in the three monomials are x and y.
The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 2.

The monomial of common literals with the smallest powers is xy2.
â€‹Hence, the greatest common factor is 3xy
2â€‹.

Question 1:

Factorize each of the following quadratic polynomials by using the method of  completing the square:
p2 + 6p + 8

Question 2:

Factorize each of the following quadratic polynomials by using the method of completing the square:
q2 − 10q + 21

Question 3:

Factorize each of the following quadratic polynomials by using the method of completing the square:
4y2 + 12y + 5

Question 4:

Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p − 16

Question 5:

Factorize each of the following quadratic polynomials by using the method of completing the square:
x2 + 12x + 20

Question 6:

Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 − 14a − 51

Question 7:

Factorize each of the following quadratic polynomials by using the method of completing the square:
a2 + 2a − 3

Question 8:

Factorize each of the following quadratic polynomials by using the method of completing the square:
4x2 − 12x + 5

Question 9:

Factorize each of the following quadratic polynomials by using the method of completing the square:
y2 − 7y + 12

Question 10:

Factorize each of the following quadratic polynomials by using the method of completing the square:
z2 − 4z − 12

Question 9:

Find the greatest common factor (GCF/HCF) of the following polynomial:
a2b3, a3b2

The common literals appearing in the three monomials are a and b.
The smallest power of x in the two monomials is 2.
The smallest power of y in the two monomials is 2
.
The monomial of common literals with the smallest powers is a2b2.
â€‹Hence, the greatest common factor is
a2b2.

Question 10:

Find the greatest common factor (GCF/HCF) of the following polynomial:
36a2b2c4, 54a5c2, 90a4b2c2

The numerical coefficients of the given monomials are 36, 54 and 90. The greatest common factor of 36, 54 and 90 is 18.
The common literals appearing in the three monomials are a and c.

The smallest power of a in the three monomials is 2.
The smallest power of c in the three monomials is 2.

The monomial of common literals with the smallest powers is a2c2.
â€‹Hence, the greatest common factor is
18a2c2.

Question 11:

Find the greatest common factor (GCF/HCF) of the following polynomial:
x3, − yx2

The common literal appearing in the two monomials is x.
The smallest power of x in both the monomials is 2.
â€‹Hence, the greatest common factor is x2.

Question 12:

Find the greatest common factor (GCF/HCF) of the following polynomial:
15a3, − 45a2, − 150a

The numerical coefficients of the given monomials are 15, -45 and -150. The greatest common factor of 15, -45 and -150 is 15.
The common literal appearing in the three monomials is a.

The smallest power of a in the three monomials is 1.
â€‹Hence, the greatest common factor is 15a.

Question 13:

Find the greatest common factor (GCF/HCF) of the following polynomial:
2x3y2, 10x2y3, 14xy

The numerical coefficients of the given monomials are 2, 10 and 14. The greatest common factor of 2, 10 and 14 is 2.
The common literals appearing in the three monomials are x and y.

The smallest power of x in the three monomials is 1.
The smallest power of y in the three monomials is 1.

The monomial of common literals with the smallest powers is xy.
â€‹Hence, the greatest common factor is 2xy.

Question 14:

Find the greatest common factor (GCF/HCF) of the following polynomial:
14x3y5, 10x5y3, 2x2y2

The numerical coefficients of the given monomials are 14, 10 and 2. The greatest common factor of 14, 10 and 2 is 2.
The common literals appearing in the three monomials are x and y.

The smallest power of x in the three monomials is 2.
The smallest power of y in the three monomials is 2.

The monomial of common literals with the smallest powers is x2y2.
â€‹Hence, the greatest common factor is 2x
2y2.

Question 15:

Find the greatest common factor of the terms in each of the following expression:
5a4 + 10a3 − 15a2

Terms are expressions separated by plus or minus signs. Here, the terms are 5a4, 10a3 and 15a2.
The numerical coefficients of the given monomials are 5, 10 and 15. The greatest common factor of 5, 10 and 15 is 5.
The common literal appearing in the three monomials is a.

The smallest power of a in the three monomials is 2.
The monomial of common literals with the smallest powers is a2.
â€‹Hence, the greatest common factor is 5a
2.

Question 16:

Find the greatest common factor of the terms in each of the following expression:
2xyz + 3x2y + 4y2

The expression has three monomials: 2xyz, 3x2y and 4y2
The numerical coefficients of the given monomials are 2, 3 and 4. The greatest common factor of 2, 3 and 4 is 1.
The common literal appearing in the three monomials is y.

The smallest power of y in the three monomials is 1.
The monomial of common literals with the smallest powers is y.
â€‹Hence, the greatest common factor is y.

Question 17:

Find the greatest common factor of the terms in each of the following expression:
3a2b2 + 4b2c2 + 12a2b2c2

The expression has three monomials: 3a2b2, 4b2c2 and 12a2b2c2
The numerical coefficients of the given monomials are 3, 4 and 12. The greatest common factor of 3, 4 and 12 is 1.
The common literal appearing in the three monomials is b.

The smallest power of b in the three monomials is 2.
The monomial of common literals with the smallest powers is b2.
â€‹Hence, the greatest common factor is b2.

Question 1:

Factorize the following:
3x − 9

The greatest common factor of the terms 3x and -9 of the expression 3x - 9 is 3.
Now.
3x = 3x
and
-9 = 3.-3
Hence, the expression 3x - 9 can be factorised as 3(x - 3).

Question 2:

Factorize the following:
5x − 15x2

The greatest common factor of the terms 5x and 15x2 of the expression 5x - 15x2 is 5x.
Now,
5x = 5x $×$
and
-15x2 = 5x $×$ -3x
Hence, the expression 5x - 15x2 can be factorised as 5x(1 - 3x)â€‹.

Question 3:

Factorize the following:
20a12b2 − 15a8b4

The greatest common factor of the terms 20a12b2 and -15a8b4 of the expression 20a12b2 - 15a8b4 is 5a8b2.
20a12b2 = 5×4×a8×a4×b2 = 5a8×b2$×$4a4 and -15a8b4 = 5×-3×a8×b2×b2 = 5a8b2 $×$ -3b2

Hence, the expression 20a12b2 - 15a8b4 can be factorised as 5a8b2(4a4-3b2)â€‹â€‹

Question 4:

Factorize the following:
72x6y7 − 96x7y6

The greatest common factor of the terms 72x6y7 and -96x7y6 of the expression 72x6y7 - 96x7y64 is 24x6y6.

Now,
72x6y7 = 24x6y6â€‹ $×$ 3y
and
-96x7y6â€‹ = 24x6y6 $×$ -4x

Hence, the expression 72x6y7 - 96x7y6 can be factorised as 24x6y6(3y - 4x)â€‹.

Question 5:

Factorize the following:
20x3 − 40x2 + 80x

The greatest common factor of the terms 20x3â€‹, -40x2â€‹ and 80xâ€‹ of the expression 20x3 - 40x2 + 80xâ€‹ is 20x.
Now,
20x3â€‹ = 20x $×$ x2
-40x2â€‹ = 20x $×$ -2x
and
80x â€‹= 20x $×$ 4
Hence, the expression 20x3 - 40x2 + 80xâ€‹ â€‹can be factorised as 20x(x2 - 2x + 4)â€‹.

Question 6:

Factorize the following:
2x3y2 − 4x2y3 + 8xy4

The greatest common factor of the terms 2x3y2, -4x2y3 and 8xy4 of the expression 2x3y2 - 4x2y3+ 8xy4y64 is 2xy2.

Now,
2x3y2 = 2xy2  $×$ x2
-4x2y3 = 2xy2 $×$ -2xy
8xy4â€‹ = 2xy2 $×$ 4y2

Hence, the expression 2x3y2 - 4x2y3 + 8xy4 â€‹can be factorised as 2xy2(x2 - 2xy + 4y2)â€‹.

Question 7:

Factorize the following:
10m3n2 + 15m4n − 20m2n3

The greatest common factor of the terms 10m3n2, 15m4n and -20m2n3 of the expression 10m3n2 + 15m4n - 20m2n3 is 5m2nâ€‹.

Now,
10m3n= 5m2n â€‹$×$ 2mn
15m4n = 5m2n $×$ 3m2
-20m2nâ€‹= 5m2n $×$ -4n2

Hence, 10m3n2 + 15m2n - 20m2n3 â€‹can be factorised as 5m2n(2mn + 3m2 - 4n2).â€‹

Question 8:

Factorize the following:
2a4b4 − 3a3b5 + 4a2b5

The greatest common factor of the terms 2a4b4, -3a3b5â€‹ and 4a2b5 of the expression 2a4b4 - 3a3b5 + 4a2b5 is a2b4â€‹.

Now,
2a4b= a2b4 $×$ 2a2
-3a3b= a2â€‹b4 $×$ -3ab
4a2b= a2â€‹b4 $×$ 4b

Hence, (2a4b4 - 3a3b5 + 4a2b5) â€‹can be factorised as [a2b4(2a2 - 3ab + 4b)]â€‹.

Question 9:

Factorize the following:
28a2 + 14a2b2 − 21a4

Question 10:

Factorize the following:
a4b − 3a2b2 − 6ab3

Question 11:

Factorize the following:
2l2mn - 3lm2n + 4lmn2

Question 12:

Factorize the following:
x4y2x2y4x4y4

Question 13:

Factorize the following:
9x2y + 3axy

Question 14:

Factorize the following:
16m − 4m2

Question 15:

Factorize the following:
−4a2 + 4ab − 4ca

Question 16:

Factorize the following:
x2yz + xy2z + xyz2

Question 17:

Factorize the following:
ax2y + bxy2 + cxyz

Question 1:

Factorize each of the following algebraic expressions:
6x(2xy) + 7y(2xy)

Question 2:

Factorize each of the following algebraic expressions:
2r(yx) + s(xy)

Question 3:

Factorize each of the following algebraic expressions:
7a(2x − 3) + 3b(2x − 3)

Question 4:

Factorize each of the following algebraic expressions:
9a(6a − 5b) −12a2(6a − 5b)

Question 5:

Factorize each of the following algebraic expressions:
5(x − 2y)2 + 3(x − 2y)

Question 6:

Factorize each of the following algebraic expressions:
16(2l − 3m)2 −12(3m − 2l)

Question 7:

Factorize each of the following algebraic expressions:
3a(x − 2y) −b(x − 2y)

Question 8:

Factorize each of the following algebraic expressions:
a2(x + y) +b2(x + y) +c2(x + y)

Question 9:

Factorize each of the following algebraic expressions:
(xy)2 + (xy)

Question 10:

Factorize each of the following algebraic expressions:
6(a + 2b) −4(a + 2b)2

Question 11:

Factorize each of the following algebraic expressions:
a(xy) + 2b(yx) + c(xy)2

Question 12:

Factorize each of the following algebraic expressions:
−4(x − 2y)2 + 8(x −2y)

Question 13:

Factorize each of the following algebraic expressions:
x3(a − 2b) + x2(a − 2b)

Question 14:

Factorize each of the following algebraic expressions:
(2x − 3y)(a + b) + (3x − 2y)(a + b)