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#### Question 1:

(i) 5x, 7x, −6x
(ii) $\frac{3}{5}x,\frac{2}{3}x,\frac{-4}{5}x$
(iii) 5a2b, −8a2b, 7a2b
(iv) $\frac{3}{4}{x}^{2},5{x}^{2},-3{x}^{2},-\frac{1}{4}{x}^{2}$
(v) x − 3y + 4z, y − 2x − 8z, 5x − 2y − 3z
(vi) 2x2 − 3y2, 5x2 + 6y2, − 3x2 − 4y2
(vii) 5x − 2x2 − 8, 8x2 − 7x − 9, 3 + 7x2 − 2x
(viii) $\frac{2}{3}a-\frac{4}{5}b+\frac{3}{5}c,-\frac{3}{4}a-\frac{5}{2}b+\frac{2}{3}c,\frac{5}{2}a+\frac{7}{4}b-\frac{5}{6}c$
(ix) $\frac{8}{5}x+\frac{11}{7}y+\frac{9}{4}xy,-\frac{3}{2}x-\frac{5}{3}y-\frac{9}{5}xy$
(x) $\frac{3}{2}{x}^{3}-\frac{1}{4}{x}^{2}+\frac{5}{3},-\frac{5}{4}{x}^{3}+\frac{3}{5}{x}^{2}-x+\frac{1}{5},-{x}^{2}+\frac{3}{8}x-\frac{8}{15}$

(i)
5x + 7x + (-6x)
= 5x + 7x -6x
= 6x

(ii)

(iii)
5a2b +( −8a2b)  + 7a2b
= 5a2b − 8a2b + 7a2b
4a2b

(iv)

(v)
Collecting like terms and adding them:

x − 3y + 4z + y − 2x − 8z + 5x − 2y − 3z
= x- 2x + 5x - 3y + y - 2y + 4z - 8z - 3z
= 4x -4y -7z

(vi) Collecting like terms and adding them:
2x2 − 3y2 + 5x2 + 6y2 + (− 3x2 − 4y2)

(vii) Collecting like terms and adding them:
5x − 2x2 − 8 +  8x2 − 7x − 9 +  3 + 7x2 − 2x

(viii) Collecting like terms and adding them:

(ix) Collecting like terms and adding them:

(x) Collecting like terms and adding them:
x+117y+94xy,32x53y9

#### Question 2:

Subtract:

(i) −8xy from 7xy
(ii) x2 from − 3x2
(iii) (x − y) from (4y − 5x)
(iv) (a2 + b2 2ab) from (a2 + b2 + 2ab)
(v) (x2 − y2) from (2x2 − 3y2 + 6xy)
(vi) (x − y + 3z) from (2zx − 3y)

(i) 7xy- (-8xy)
= 7xy+ 8xy
= 15xy

(ii)  - 3x2 - x2
= -4x2

(iii)  (4y - 5x) - (x- y)
= 4y - 5x - x + y
= 5y - 6x

(iv)
(a2 + b2 + 2ab) - (a2 + b2 2ab)
=     (Collecting like terms and adding them)
= 4ab

(v)
(2x2 − 3y2 + 6xy) -  (x2y2)
(Collecting like terms and adding them)

(vi)  (2z -x -3y) - (x - y +3z)
= 2z -3z -x -x -3y +y       (Collecting like terms and adding them)
= -z -2x - 2y

#### Question 3:

Subtract (2a 3b + 4c) from the sum of (a + 3b − 4c), (4ab + 9c) and (−2b + 3ca).

(a + 3b − 4c) + (4ab + 9c) + (−2b + 3ca)
= a + 4a - a + 3b -b -2b -4c +9c + 3c
= 4a + 8c

Now,  (4a + 8c ) - (2a 3b + 4c)
= 4a - 2a + 3b + 8c - 4c
= 2a + 3b + 4c

#### Question 4:

Subtract the sum of (8m − 7n + 6p2) and (−3m − 4np2) from the sum of (2m + 4n − 3p2) and (− mn − p2).

(8m − 7n + 6p2) + (−3m − 4np2)

(2m + 4n − 3p2) + (− mn − p2).

#### Question 5:

Subtract the sum of (8a − 6a2 + 9) and (−10a − 8 + 8a2) from −3.

(8a − 6a2 + 9)+  (−10a − 8 + 8a2)

Collecting like terms and adding them:

#### Question 6:

Simplify:

(i) (5x −9y) − (−7x + y)
(ii) $\left({x}^{2}-x\right)-\frac{1}{2}\left(x-3+3{x}^{2}\right)$
(iii) [7 − 2x + 5y − (x − y)] − (5x + 3y − 7)
(iv) $\left(\frac{1}{3}{y}^{2}-\frac{4}{7}y+5\right)-\left(\frac{2}{7}y-\frac{2}{3}{y}^{2}+2\right)-\left(\frac{1}{7}y-3+2{y}^{2}\right)$

Collecting like terms and adding them:

(i)  5x + 7x - 9y -y
= 12x -10y

(ii)

(iii)  7 + 7 - 2x -x - 5x + 5y + y - 3y
= 14 - 8x -3y

(iv)

#### Question 1:

Find the products:

3a2 × 8a4

3a2 × 8a4

#### Question 2:

Find the products:

−6x3 × 5x2

−6x3 × 5x2
$=\left(-6×5\right)×\left({\mathrm{x}}^{3}×{\mathrm{x}}^{2}\right)\phantom{\rule{0ex}{0ex}}=\left(-30\right)×\left({\mathrm{x}}^{\left(3+2\right)}\right)\phantom{\rule{0ex}{0ex}}=-30{\mathrm{x}}^{5}\phantom{\rule{0ex}{0ex}}$

#### Question 3:

Find the products:

(−4ab) × (−3a2bc)

(−4ab) × (−3a2bc)

#### Question 4:

Find the products:

(2a2b3) × (−3a3b)

(2a2b3) × (−3a3b)
$=\left(2×\left(-3\right)\right)×\left({\mathrm{a}}^{2}×{\mathrm{a}}^{3}×{\mathrm{b}}^{3}×\mathrm{b}\right)\phantom{\rule{0ex}{0ex}}=\left(-6\right)×\left({\mathrm{a}}^{\left(2+3\right)}×{\mathrm{b}}^{\left(3+1\right)}\right)\phantom{\rule{0ex}{0ex}}=-6{\mathrm{a}}^{5}{\mathrm{b}}^{4}$

#### Question 5:

Find the products:

$\frac{2}{3}{x}^{2}y×\frac{3}{5}x{y}^{2}$

$=\left(\frac{2}{3}×\frac{3}{5}\right)×\left({\mathrm{x}}^{2}×\mathrm{x}×\mathrm{y}×{\mathrm{y}}^{2\right)}\right)\phantom{\rule{0ex}{0ex}}=\frac{2}{5}×{\mathrm{x}}^{\left(2+1\right)}×{\mathrm{y}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=\frac{2}{5}{\mathrm{x}}^{3}{\mathrm{y}}^{3}$

#### Question 6:

Find the products:

$\left(\frac{-3}{4}a{b}^{3}\right)×\left(\frac{-2}{3}{a}^{2}{b}^{4}\right)$

$=\left(\frac{-3}{4}×\frac{-2}{3}\right)×\left(\mathrm{a}×{\mathrm{a}}^{2}×{\mathrm{b}}^{3}×{\mathrm{b}}^{4}\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{2}×{\mathrm{a}}^{\left(1+2\right)}×{\mathrm{b}}^{\left(3+4\right)}\phantom{\rule{0ex}{0ex}}=\frac{1}{2}{\mathrm{a}}^{3}{\mathrm{b}}^{7}$

#### Question 7:

Find the products:

$\left(\frac{-1}{27}{a}^{2}{b}^{2}\right)×\left(\frac{-9}{2}{a}^{3}b{c}^{2}\right)$

$=\left(\frac{-1}{27}×\frac{-9}{2}\right)×\left({\mathrm{a}}^{2}×{\mathrm{a}}^{3}×{\mathrm{b}}^{2}×\mathrm{b}×{\mathrm{c}}^{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{1}{6}×{\mathrm{a}}^{\left(2+3\right)}×{\mathrm{b}}^{\left(2+1\right)}×{\mathrm{c}}^{2}\phantom{\rule{0ex}{0ex}}=\frac{1}{6}{\mathrm{a}}^{5}{\mathrm{b}}^{3}{\mathrm{c}}^{2}$

#### Question 8:

Find the products:

$\left(\frac{-13}{5}a{b}^{2}c\right)×\left(\frac{7}{3}{a}^{2}b{c}^{2}\right)$

$=\left(\frac{-13}{5}×\frac{7}{3}\right)×\left(\mathrm{a}×{\mathrm{a}}^{2}×{\mathrm{b}}^{2}×\mathrm{b}×\mathrm{c}×{\mathrm{c}}^{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{-91}{15}{\mathrm{a}}^{\left(1+2\right)}×{\mathrm{b}}^{\left(2+1\right)}×{\mathrm{c}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=\frac{-91}{15}{\mathrm{a}}^{3}{\mathrm{b}}^{3}{\mathrm{c}}^{3}$

#### Question 9:

Find the products:

$\left(\frac{-18}{5}{x}^{2}z\right)×\left(\frac{-25}{6}x{z}^{2}y\right)$

$=\left(-\frac{18}{5}×\frac{-25}{6}\right)×\left({\mathrm{x}}^{2}×\mathrm{x}×\mathrm{z}×{\mathrm{z}}^{2}×\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=15×{\mathrm{x}}^{\left(2+1\right)}×\mathrm{y}×{\mathrm{z}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=15{\mathrm{x}}^{3}{\mathrm{yz}}^{3}$

#### Question 10:

Find the products:

$\left(\frac{-3}{14}x{y}^{4}\right)×\left(\frac{7}{6}{x}^{3}y\right)$

$=\left(\frac{-3}{14}×\frac{7}{6}\right)×\left(\mathrm{x}×{\mathrm{x}}^{3}×{\mathrm{y}}^{4}×\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=\frac{-1}{4}{\mathrm{x}}^{\left(1+3\right)}×{\mathrm{y}}^{\left(4+1\right)}\phantom{\rule{0ex}{0ex}}=\frac{-1}{4}{\mathrm{x}}^{4}{\mathrm{y}}^{5}$

#### Question 11:

Find the products:

$\left(\frac{-7}{5}{x}^{2}y\right)×\left(\frac{3}{2}x{y}^{2}\right)×\left(\frac{-6}{5}{x}^{3}{y}^{3}\right)$

$=\left(\frac{-7}{5}×\frac{3}{2}×\frac{-6}{5}\right)×\left({\mathrm{x}}^{2}×\mathrm{x}×{\mathrm{x}}^{3}×\mathrm{y}×{\mathrm{y}}^{2}×{\mathrm{y}}^{3}\right)\phantom{\rule{0ex}{0ex}}=\frac{63}{25}×{\mathrm{x}}^{\left(2+1+3\right)}×{\mathrm{y}}^{\left(1+2+3\right)}\phantom{\rule{0ex}{0ex}}=\frac{63}{25}{\mathrm{x}}^{6}{\mathrm{y}}^{6}$

#### Question 12:

Find the products:

(2a2b) × (−5ab2c) × (−6bc2)

$=\left(2×\left(-5\right)×\left(-6\right)\right)×\left({\mathrm{a}}^{2}×\mathrm{a}×\mathrm{b}×{\mathrm{b}}^{2}×\mathrm{b}×\mathrm{c}×{\mathrm{c}}^{2}\right)\phantom{\rule{0ex}{0ex}}=60×{\mathrm{a}}^{\left(2+1\right)}×{\mathrm{b}}^{\left(1+2+1\right)}×{\mathrm{c}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=60{\mathrm{a}}^{3}{\mathrm{b}}^{4}{\mathrm{c}}^{3}$

#### Question 13:

Find the products:

(−4x2) × (−6xy2) × (−3y)

$=\left(-4×\left(-6\right)×\left(-3\right)\right)×\left({\mathrm{x}}^{2}×\mathrm{x}×{\mathrm{y}}^{2}×\mathrm{y}\right)\phantom{\rule{0ex}{0ex}}=-72×{\mathrm{x}}^{\left(2+1\right)}×{\mathrm{y}}^{\left(2+1\right)}\phantom{\rule{0ex}{0ex}}=-72{\mathrm{x}}^{3}{\mathrm{y}}^{3}$

#### Question 14:

Find the products:

$\left(\frac{-3}{5}{s}^{2}t\right)×\left(\frac{15}{7}s{t}^{2}u\right)×\left(\frac{7}{9}s{u}^{2}\right)$

$=\left(\frac{-3}{5}×\frac{15}{7}×\frac{7}{9}\right)×\left({\mathrm{s}}^{2}×\mathrm{s}×\mathrm{s}×\mathrm{t}×{\mathrm{t}}^{2}×\mathrm{u}×{\mathrm{u}}^{2}\right)\phantom{\rule{0ex}{0ex}}=-1×{\mathrm{s}}^{\left(2+1+1\right)}×{\mathrm{t}}^{\left(1+2\right)}×{\mathrm{u}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=-{\mathrm{s}}^{4}{\mathrm{t}}^{3}{\mathrm{u}}^{3}$

#### Question 15:

Find the products:

$\left(\frac{-2}{7}{u}^{4}v\right)×\left(\frac{-14}{5}u{v}^{3}\right)×\left(\frac{-3}{4}{u}^{2}{v}^{3}\right)$

$=\left(\frac{-2}{7}×\frac{-14}{5}×\frac{-3}{4}\right)×\left({\mathrm{u}}^{4}×\mathrm{u}×{\mathrm{u}}^{2}×\mathrm{v}×{\mathrm{v}}^{3}×{\mathrm{v}}^{3}\right)\phantom{\rule{0ex}{0ex}}=\frac{-3}{5}×{\mathrm{u}}^{\left(4+1+2\right)}×{\mathrm{v}}^{\left(1+3+3\right)}\phantom{\rule{0ex}{0ex}}=\frac{-3}{5}{\mathrm{u}}^{7}{\mathrm{v}}^{7}$

#### Question 16:

Find the products:

(ab2) × (−b2c) × (−a2c3) × (−3abc)

$=\left(-3×-1×-1\right)×\left(\mathrm{a}×{\mathrm{a}}^{2}×\mathrm{a}×{\mathrm{b}}^{2}×{\mathrm{b}}^{2}×\mathrm{b}×\mathrm{c}×{\mathrm{c}}^{3}×\mathrm{c}\phantom{\rule{0ex}{0ex}}=-3×{\mathrm{a}}^{\left(1+2+1\right)}×{\mathrm{b}}^{\left(2+2+1\right)}×{\mathrm{c}}^{\left(1+4+1\right)}\phantom{\rule{0ex}{0ex}}=-3{\mathrm{a}}^{4}{\mathrm{b}}^{5}{\mathrm{c}}^{5}$

#### Question 17:

Find the products:

$\left(\frac{4}{3}{x}^{2}yz\right)×\left(\frac{1}{3}{y}^{2}zx\right)×\left(-6xy{z}^{2}\right)$

$=\left(\frac{4}{3}×\frac{1}{3}×\left(-6\right)\right)×\left({\mathrm{x}}^{2}×\mathrm{x}×\mathrm{x}×\mathrm{y}×{\mathrm{y}}^{2}×\mathrm{y}×\mathrm{z}×\mathrm{z}×{\mathrm{z}}^{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{-8}{3}×{\mathrm{x}}^{\left(2+1+1\right)}×{\mathrm{y}}^{\left(1+2+1\right)}×{\mathrm{z}}^{\left(1+1+2\right)}\phantom{\rule{0ex}{0ex}}=\frac{-8}{3}{\mathrm{x}}^{4}{\mathrm{y}}^{4}{\mathrm{z}}^{4}$

#### Question 18:

Multiply and verify your result for a = 2 and b = 3.

$\frac{-2}{3}{\mathrm{a}}^{2}\mathrm{b}×\frac{6}{5}{\mathrm{a}}^{3}{\mathrm{b}}^{2}\phantom{\rule{0ex}{0ex}}=\left(\frac{-2}{3}×\frac{6}{5}\right)×\left({\mathrm{a}}^{2}×{\mathrm{a}}^{3}×\mathrm{b}×{\mathrm{b}}^{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{-4}{5}×{\mathrm{a}}^{\left(2+3\right)}×{\mathrm{b}}^{\left(1+2\right)}\phantom{\rule{0ex}{0ex}}=\frac{-4}{5}{\mathrm{a}}^{5}{\mathrm{b}}^{3}\phantom{\rule{0ex}{0ex}}$

When a =2 and b =3, we get:

L.H.S. = R.H.S.

Hence, the result is verified.

#### Question 19:

Multiply and verify your result for x = 3 and y = 2.

#### Question 20:

Find the value of (2.3a5b2) × (1.2a2b2), when a = 1 and b = 0.5.

#### Question 21:

Find the value of (−8u2v6) × (−20uv) for u = 2.5 and v = 1.

#### Question 22:

Find the product and verify the result for a = 1, b = 2 and c = 3.

$\left(\frac{2}{5}{a}^{2}b\right)×\left(-15{b}^{2}ac\right)×\left(-\frac{1}{2}{c}^{2}\right)$

#### Question 23:

Find the product and verify the result for a = 1, b = 2 and c = 3.

$\left(\frac{1}{4}abc\right)×\left(-6{b}^{2}c\right)×\left(-\frac{1}{3}{c}^{3}\right)$

#### Question 24:

Find the product and verify the result for a = 1, b = 2 and c = 3.

$\left(\frac{4}{9}ab{c}^{3}\right)×\left(\frac{-27}{5}{a}^{3}{b}^{2}\right)×\left(-8{b}^{3}c\right)$

#### Question 25:

Find the product and verify the result for a = 1, b = 2 and c = 3.

$\left(\frac{-4}{7}{a}^{2}b\right)×\left(\frac{-2}{3}{b}^{2}c\right)×\left(\frac{-7}{6}{c}^{2}a\right)$

#### Question 1:

Find the product:

4a(3a + 7b)

#### Question 2:

Find the product:

5a(6a − 3b)

#### Question 3:

Find the product:

8a2(2a + 5b)

#### Question 4:

Find the product:

9x2(5x + 7)

#### Question 5:

Find the product:

ab(a2 b2)

#### Question 6:

Find the product:

2x2(3x − 4x2)

#### Question 7:

Find the product:

$\frac{3}{5}{m}^{2}n\left(m+5n\right)$

#### Question 8:

Find the product:

−17x2(3x − 4)

#### Question 9:

Find the product:

$\frac{7}{2}{x}^{2}\left(\frac{4}{7}x+2\right)$

#### Question 10:

Find the product:

−4x2y(3x2 − 5y)

#### Question 11:

Find the product:

$\frac{-4}{27}xyz\left(\frac{9}{2}{x}^{2}yz-\frac{3}{4}xy{z}^{2}\right)$

#### Question 12:

Find the product:

9t2(t + 7t3)

#### Question 13:

Find the product:

10a2(0.1a − 0.5b)

#### Question 14:

Find the product:

1.5a(10a2 − 100ab2)

#### Question 15:

Find the product:

$\frac{2}{3}abc\left({a}^{2}+{b}^{2}-3{c}^{2}\right)$

#### Question 16:

Find the product 24x2(1−2x) and evaluate it for x = 2.

#### Question 17:

Find the product ab(a2+b2) and evaluate it for a = 2 and b = $\frac{1}{2}$.

#### Question 18:

Find the product s (s2 st) and find its value for s = 2 and t = 3.

#### Question 19:

Find the product −3y(xy + y2) and find its value for x = 4 and y = 5.

#### Question 20:

Simplify

a(b − c) + b(c − a) + c(a − b)

#### Question 21:

Simplify

a(b − c− b(c − a) − c(a − b)

#### Question 22:

Simplify

3x2 + 2(x + 2) 3x(2x + 1)

#### Question 23:

Simplify

x(x + 4) + 3x(2x2 − 1) + 4x2 + 4

#### Question 24:

Simplify

2x2 + 3x(1 − 2x3) + x(x + 1)

#### Question 25:

Simplify

a2b(a b2) + ab2(4ab − 2a2) −a3b(1 − 2b)

#### Question 26:

Simplify

4st(s t) −6s2(tt2) −3t2 (2s2 s) +2st (st)

#### Question 1:

Find the product:

(5x + 7)(3x + 4)

#### Question 2:

Find the product:

(4x − 3)(2x + 5)

#### Question 3:

Find the product:

(− 6)(4x + 9)

#### Question 4:

Find the product:

(5y − 1)(3y − 8)

#### Question 5:

Find the product:

(7x + 2y)(x + 4y)

#### Question 6:

Find the product:

(9x + 5y)(4x + 3y)

#### Question 7:

Find the product:

(3m − 4n)(2m − 3n)

#### Question 8:

Find the product:

(0.8x −  0.5y)(1.5x −  3y)

#### Question 9:

Find the product:

$\left(\frac{1}{5}x+2y\right)\left(\frac{2}{3}x-y\right)$

#### Question 10:

Find the product:

$\left(\frac{2}{5}x-\frac{1}{2}y\right)\left(10x-8y\right)$

#### Question 11:

Find the product:

$\left(\frac{3}{4}a+\frac{2}{3}b\right)\left(4a+3b\right)$

#### Question 12:

Find the product:

(x2a2)(xa)

#### Question 13:

Find the product:

(3p2 + q2)(2p2 − 3q2)

#### Question 14:

Find the product:

(2x2 − 5y2)(x2 + 3y2)

#### Question 15:

Find the product:

(x3y3)(x2 + y2)

#### Question 16:

Find the product:

(x4 + y4)(x2 − y2)

#### Question 17:

Find the product:

$\left({x}^{4}+\frac{1}{{x}^{4}}\right)\left(x+\frac{1}{x}\right)$

#### Question 18:

Find the product:

(x2y2)(x + 2y)

#### Question 19:

Find the product:

(2x + 3y − 5)(x + y)

#### Question 20:

Find the product:

(3x + 2y − 4)(xy)

By column method:

#### Question 21:

Find the product:

(x2 − 3x + 7)(2x + 3)

By column method:

#### Question 22:

Find the product:

(3x2 + 5x − 9)(3x −9)

By column method:

#### Question 23:

Find the product:

(9x2 x + 15)(x2 − 3)

By column method:

#### Question 24:

Find the product:

(x2 + xy + y2)(xy)

By column method:

#### Question 25:

Find the product:

(x2 xy + y2)(x + y)

By column method:

#### Question 26:

Find the product:

(x2 − 5x + 8)(x2 + 2)

By column method:

#### Question 27:

Simplify

(3x + 4)(2x − 3) + (5x − 4)(x + 2)

(3x +4)(2x -3)

∴ (3x + 4)(2x − 3) + (5x − 4)(x + 2)

#### Question 28:

Simplify

(5x − 3)(x + 4) − (2x + 5)(3x − 4)

(5x-3)(x+4)

(2x +5)(3x-4)

∴ (5x − 3)(x + 4) − (2x + 5)(3x − 4)

#### Question 29:

Simplify

(9x − 7)(2x − 5) − (3x − 8)(5x − 3)

#### Question 30:

Simplify

(2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

(2x +5y)(3x+4y)

∴ (2x + 5y)(3x + 4y) − (7x + 3y)(2x − y)

#### Question 31:

Simplify

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

(3x2 + 5x − 7)(x − 1)

By column method:

(x2 − 2x + 3)(x + 4)

By column method:

(3x2 + 5x − 7)(x − 1) − (x2 − 2x + 3)(x + 4)

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