Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 7 Factorisation are provided here with simple step-by-step explanations. These solutions for Factorisation are extremely popular among Class 8 students for Math Factorisation Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 99:
Question 1:
Factorise:
(i) 12x + 15
(ii) 14m − 21
(iii) 9n − 12n2
Answer:
(i)
(ii)
(iii)
Page No 99:
Question 2:
Factorise:
(i) 16a2 − 24ab
(ii) 15ab2 − 20a2b
(iii) 12x2y3 − 21x3y2
Answer:
(i) H.C.F. of and is .
∴
(ii) H.C.F. of and is .
∴
(iii) H.C.F. of and is .
∴
Page No 99:
Question 3:
Factorise:
(i) 24x3 − 36x2y
(ii) 10x3 − 15x2
(iii) 36x3y − 60x2y3z
Answer:
(i) H.C.F. of and is .
∴
(ii) H.C.F. of and is .
∴
(iii) H.C.F. of and is .
∴
Page No 99:
Question 4:
Factorise:
(i) 9x3 − 6x2 + 12x
(ii) 8x2 − 72xy + 12x
(iii) 18a3b3 − 27a2b3 + 36a3b2
Answer:
(i) H.C.F. of , and is .
∴
(ii) H.C.F. of , and is .
∴
(iii) H.C.F. of , and is .
∴
Page No 99:
Question 5:
Factorise:
(i) 14x3 + 21x4y − 28x2y2
(ii) −5 − 10t + 20t2
Answer:
(i) H.C.F. of , and is .
∴
(ii) H.C.F. of , and is 5.
∴
Page No 99:
Question 6:
Factorise:
(i) x(x + 3) + 5(x + 3)
(ii) 5x(x − 4) − 7(x − 4)
(iii) 2m(1 − n) + 3(1 − n)
Answer:
(i)
(ii)
(iii)
Page No 99:
Question 7:
Factorise:
6a(a − 2b) + 5b(a − 2b)
Answer:
We have:
Page No 99:
Question 8:
Factorise:
x3(2a − b) + x2(2a − b)
Answer:
We have:
Page No 99:
Question 9:
Factorise:
9a(3a − 5b) − 12a2(3a − 5b)
Answer:
We have:
Page No 99:
Question 10:
Factorise:
(x + 5)2 − 4(x + 5)
Answer:
We have:
∴
Page No 99:
Question 11:
Factorise:
3(a − 2b)2 − 5(a − 2b)
Answer:
∴
Page No 99:
Question 12:
Factorise:
2a + 6b − 3(a + 3b)2
Answer:
We have:
∴
Page No 99:
Question 13:
Factorise:
16(2p − 3q)2 − 4(2p − 3q)
Answer:
We have:
∴
Page No 99:
Question 14:
Factorise:
x(a − 3) + y(3 − a)
Answer:
We have:
∴
Page No 99:
Question 15:
Factorise:
12(2x − 3y)2 − 16(3y − 2x)
Answer:
We have:
Page No 99:
Question 16:
Factorise:
(x + y)(2x + 5) − (x + y)(x + 3)
Answer:
We have:
Page No 99:
Question 17:
Factorise:
ar + br + at + bt
Answer:
By grouping the terms:
∴
Page No 99:
Question 18:
Factorise:
x2 − ax − bx + ab
Answer:
By suitably arranging the terms:
∴
Page No 99:
Question 19:
Factorise:
ab2 − bc2 − ab + c2
Answer:
By suitably arranging the terms:
∴
Page No 99:
Question 20:
Factorise:
x2 − xz + xy − yz
Answer:
By suitably arranging the terms:
∴
Page No 99:
Question 21:
Factorise:
6ab − b2 + 12ac − 2bc
Answer:
By suitably arranging the terms:
∴
Page No 99:
Question 22:
Factorise:
(x − 2y)2 + 4x − 8y
Answer:
We have:
∴
Page No 99:
Question 23:
Factorise:
y2 − xy(1 − x) − x3
Answer:
We have:
∴
Page No 99:
Question 24:
Factorise:
(ax + by)2 + (bx − ay)2
Answer:
We have:
∴
Page No 99:
Question 25:
Factorise:
ab2 + (a − 1)b − 1
Answer:
We have:
∴
Page No 99:
Question 26:
Factorise:
x3 − 3x2 + x − 3
Answer:
We have:
∴
Page No 99:
Question 27:
Factorise:
ab(x2 + y2) − xy(a2 + b2)
Answer:
We have:
∴
Page No 99:
Question 28:
Factorise:
x2 − x(a + 2b) + 2ab
Answer:
We have:
∴
Page No 100:
Question 1:
Factorise:
x2 − 36
Answer:
We have:
∴
Page No 100:
Question 2:
Factorise:
4a2 − 9
Answer:
We have:
∴
Page No 100:
Question 3:
Factorise:
81 − 49x2
Answer:
We have:
∴
Page No 100:
Question 4:
Factorise:
4x2 − 9y2
Answer:
We have:
∴
Page No 100:
Question 5:
Factorise:
16a2 − 225b2
Answer:
We have:
∴
Page No 100:
Question 6:
Factorise:
9a2b2 − 25
Answer:
We have:
∴
Page No 100:
Question 7:
Factorise:
16a2 − 144
Answer:
We have:
∴
Page No 100:
Question 8:
Factorise:
63a2 − 112b2
Answer:
We have:
∴
Page No 100:
Question 9:
Factorise:
20a2 − 45b2
Answer:
We have:
∴
Page No 100:
Question 10:
Factorise:
12x2 − 27
Answer:
We have:
∴
Page No 100:
Question 11:
Factorise:
x3 − 64x
Answer:
We have:
∴
Page No 100:
Question 12:
Factorise:
16x5 − 144x3
Answer:
We have:
∴
Page No 100:
Question 13:
Factorise:
3x5 − 48x3
Answer:
We have:
∴
Page No 100:
Question 14:
Factorise:
16p3 − 4p
Answer:
We have:
∴
Page No 100:
Question 15:
Factorise:
63a2b2 − 7
Answer:
We have:
∴
Page No 100:
Question 16:
Factorise:
1 − (b − c)2
Answer:
We have:
∴
Page No 100:
Question 17:
Factorise:
(2a + 3b)2 − 16c2
Answer:
We have:
∴
Page No 100:
Question 18:
Factorise:
(l + m)2 − (l − m)2
Answer:
We have:
∴
Page No 100:
Question 19:
Factorise:
(2x + 5y)2 − 1
Answer:
We have:
∴
Page No 100:
Question 20:
Factorise:
36c2 − (5a + b)2
Answer:
We have:
∴
Page No 100:
Question 21:
Factorise:
(3x − 4y)2 − 25z2
Answer:
We have:
∴
Page No 100:
Question 22:
Factorise:
x2 − y2 − 2y − 1
Answer:
We have:
∴
Page No 100:
Question 23:
Factorise:
25 − a2 − b2 − 2ab
Answer:
We have:
∴
Page No 100:
Question 24:
Factorise:
25a2 − 4b2 + 28bc − 49c2
Answer:
We have:
∴
Page No 100:
Question 25:
Factorise:
9a2 − b2 + 4b − 4
Answer:
We have:
∴
Page No 100:
Question 26:
Factorise:
100 − (x − 5)2
Answer:
We have:
∴
Page No 100:
Question 27:
Factorise:
Evaluate {(405)2 − (395)2}.
Answer:
We have:
∴
Page No 100:
Question 28:
Factorise:
Evaluate {(7.8)2 − (2.2)2}.
Answer:
We have:
∴
Page No 101:
Question 1:
Factorise:
x2 + 8x + 16
Answer:
We have:
∴
Page No 101:
Question 2:
Factorise:
x2 + 14x + 49
Answer:
We have:
∴
Page No 101:
Question 3:
Factorise:
1 + 2x + x2
Answer:
We have:
∴
Page No 101:
Question 4:
Factorise:
9 + 6z + z2
Answer:
We have;
∴
Page No 101:
Question 5:
Factorise:
x2 + 6ax + 9a2
Answer:
We have:
∴
Page No 101:
Question 6:
Factorise:
4y2 + 20y + 25
Answer:
We have:
∴
Page No 101:
Question 7:
Factorise:
36a2 + 36a + 9
Answer:
We have:
∴
Page No 101:
Question 8:
Factorise:
9m2 + 24m + 16
Answer:
We have:
∴
Page No 101:
Question 9:
Factorise:
z2 + z +
Answer:
We have:
∴
Page No 101:
Question 10:
Factorise:
49a2 + 84ab + 36b2
Answer:
We have:
∴
Page No 101:
Question 11:
Factorise:
p2 − 10p + 25
Answer:
We have:
∴
Page No 101:
Question 12:
Factorise:
121a2 − 88ab + 16b2
Answer:
We have:
∴
Page No 101:
Question 13:
Factorise:
1 − 6x + 9x2
Answer:
We have:
∴
Page No 101:
Question 14:
Factorise:
9y2 − 12y + 4
Answer:
We have:
∴
Page No 101:
Question 15:
Factorise:
16x2 − 24x + 9
Answer:
We have:
∴
Page No 101:
Question 16:
Factorise:
m2 − 4mn + 4n2
Answer:
We have:
∴
Page No 101:
Question 17:
Factorise:
a2b2 − 6abc + 9c2
Answer:
We have:
Page No 101:
Question 18:
Factorise:
m4 + 2m2n2 + n4
Answer:
We have:
∴
Page No 101:
Question 19:
Factorise:
(l + m)2 − 4lm
Answer:
We have:
∴
Page No 102:
Question 1:
Factorise:
x2 + 5x + 6
Answer:
Page No 102:
Question 2:
Factorise:
y2 + 10y + 24
Answer:
Page No 102:
Question 3:
Factorise:
z2 + 12z + 27
Answer:
Page No 102:
Question 4:
Factorise:
p2 + 6p + 8
Answer:
Page No 102:
Question 5:
Factorise:
x2 + 15x + 56
Answer:
Page No 102:
Question 6:
Factorise:
y2 + 19y + 60
Answer:
Page No 102:
Question 7:
Factorise:
x2 + 13x + 40
Answer:
Page No 102:
Question 8:
Factorise:
q2 − 10q + 21
Answer:
Page No 102:
Question 9:
Factorise:
p2 + 6p − 16
Answer:
Page No 102:
Question 10:
Factorise:
x2 − 10x + 24
Answer:
Page No 102:
Question 11:
Factorise:
x2 − 23x + 42
Answer:
Page No 102:
Question 12:
Factorise:
x2 − 17x + 16
Answer:
Page No 103:
Question 13:
Factorise:
y2 − 21y + 90
Answer:
Page No 103:
Question 14:
Factorise:
x2 − 22x + 117
Answer:
Page No 103:
Question 15:
Factorise:
x2 − 9x + 20
Answer:
Page No 103:
Question 16:
Factorise:
x2 + x − 132
Answer:
Page No 103:
Question 17:
Factorise:
x2 + 5x − 104
Answer:
Page No 103:
Question 18:
Factorise:
y2 + 7y − 144
Answer:
Page No 103:
Question 19:
Factorise:
z2 + 19z − 150
Answer:
Page No 103:
Question 20:
Factorise:
y2 + y − 72
Answer:
Page No 103:
Question 21:
Factorise:
a2 + 6a − 91
Answer:
Page No 103:
Question 22:
Factorise:
p2 − 4p − 77
Answer:
Page No 103:
Question 23:
Factorise:
x2 − 7x − 30
Answer:
Page No 103:
Question 24:
Factorise:
x2 − 11x − 42
Answer:
Page No 103:
Question 25:
Factorise:
x2 − 5x − 24
Answer:
Page No 103:
Question 26:
Factorise:
y2 − 6y − 135
Answer:
Page No 103:
Question 27:
Factorise:
z2 − 12z − 45
Answer:
Page No 103:
Question 28:
Factorise:
x2 − 4x − 12
Answer:
Page No 103:
Question 29:
Factorise:
3x2 + 10x + 8
Answer:
Page No 103:
Question 30:
Factorise:
3y2 + 14y + 8
Answer:
Page No 103:
Question 31:
Factorise:
3z2 − 10z + 8
Answer:
Page No 103:
Question 32:
Factorise:
2x2 + x − 45
Answer:
Page No 103:
Question 33:
Factorise:
6p2 + 11p − 10
Answer:
Page No 103:
Question 34:
Factorise:
2x2 − 17x − 30
Answer:
Page No 103:
Question 35:
Factorise:
7y2 − 19y − 6
Answer:
Page No 103:
Question 36:
Factorise:
28 − 31x − 5x2
Answer:
Page No 103:
Question 37:
Factorise:
3 + 23z − 8z2
Answer:
Page No 103:
Question 38:
Factorise:
6x2 − 5x − 6
Answer:
Page No 103:
Question 39:
Factorise:
3m2 + 24m + 36
Answer:
Page No 103:
Question 40:
Factorise:
4n2 − 8n + 3
Answer:
Page No 103:
Question 41:
Factorise:
6x2 − 17x − 3
Answer:
Page No 103:
Question 42:
Factorise:
7x2 − 19x − 6
Answer:
Page No 103:
Question 1:
Tick (✓) the correct answer:
(7a2 − 63b2) = ?
(a) (7a − 9b)(9a + 7b)
(b) (7a − 9b)(7a + 9b)
(c) 9(a − 3b)(a + 3b)
(d) 7(a − 3b)(a + 3b)
Answer:
(d) 7(a − 3b)(a + 3b)
Page No 103:
Question 2:
Tick (✓) the correct answer:
(2x − 32x3) = ?
(a) 2(x − 4)(x + 4)
(b) 2x(1 − 2x)2
(c) 2x(1 + 2x)2
(d) 2x(1 − 4x)(1 + 4x)
Answer:
(d) 2x(1 − 4x)(1 + 4x)
Page No 103:
Question 3:
Tick (✓) the correct answer:
x3 − 144x = ?
(a) x(x − 12)2
(b) x(x + 12)2
(c) x(x − 12)(x + 12)
(d) none of these
Answer:
(c) x(x − 12)(x + 12)
Page No 103:
Question 4:
Tick (✓) the correct answer:
(2 − 50x2) = ?
(a) 2(1 − 5x)2
(b) 2(1 + 5x)2
(c) (2 − 5x)(2 + 5x)
(d) 2(1 − 5x)(1 + 5x)
Answer:
(d) 2(1 − 5x)(1 + 5x)
Page No 103:
Question 5:
Tick (✓) the correct answer:
a2 + bc + ab + ac = ?
(a) (a + b)(a + c)
(b) (a + b)(b + c)
(c) (b + c)(c + a)
(d) a(a + b + c)
Answer:
(a) (a + b)(a + c)
Page No 103:
Question 6:
Tick (✓) the correct answer:
pq2 + q(p − 1) − 1 = ?
(a) (pq + 1)(q − 1)
(b) p(q + 1)(q − 1)
(c) q(p − 1)(q + 1)
(d) (pq − 1) (q + 1)
Answer:
(d) (pq − 1) (q + 1)
Page No 103:
Question 7:
Tick (✓) the correct answer:
ab − mn + an − bm = ?
(a) (a − b)(m − n)
(b) (a − m)(b + n)
(c) (a − n)(m + b)
(d) (m − a)(n − b)
Answer:
(b) (a − m)(b + n)
Page No 103:
Question 8:
Tick (✓) the correct answer:
ab − a − b + 1 = ?
(a) (a − 1)(b − 1)
(b) (1 − a)(1 − b)
(c) (a − 1)(1 − b)
(d) (1 − a)(b − 1)
Answer:
(a) (a − 1)(b − 1)
Page No 103:
Question 9:
Tick (✓) the correct answer:
x2 − xz + xy − yz = ?
(a) (x − y)(x + z)
(b) (x − y)(x − z)
(c) (x + y)(x − z)
(d) (x − y)(z − x)
Answer:
(c) (x + y)(x − z)
Page No 104:
Question 10:
Tick (✓) the correct answer:
(12m2 − 27) = ?
(a) (2m − 3)(3m − 9)
(b) 3(2m − 9)(3m − 1)
(c) 3(2m − 3)(2m + 3)
(d) none of these
Answer:
(c) 3(2m − 3)(2m + 3)
Page No 104:
Question 11:
Tick (✓) the correct answer:
x3 − x = ?
(a) x(x2 − x)
(b) x(x − x2)
(c) x(1 + x)(1 − x)
(d) x(x + 1)(x − 1)
Answer:
(d) x(x + 1)(x − 1)
Page No 104:
Question 12:
Tick (✓) the correct answer:
1 − 2ab − (a2 + b2) = ?
(a) (1 + a − b)(1 + a + b)
(b) (1 + a + b)(1 − a + b)
(c) (1 + a + b)(1 − a − b)
(d) (1 + a − b)(1 − a + b)
Answer:
(c) (1 + a + b)(1 − a − b)
Page No 104:
Question 13:
Tick (✓) the correct answer:
x2 + 6x + 8 = ?
(a) (x + 3)(x + 5)
(b) (x + 3)(x + 4)
(c) (x + 2)(x + 4)
(d) (x + 1)(x + 8)
Answer:
(c) (x + 2)(x + 4)
Page No 104:
Question 14:
Tick (✓) the correct answer:
x2 + 4x − 21 = ?
(a) (x − 7)(x + 3)
(b) (x + 7)(x − 3)
(c) (x − 7)(x − 3)
(d) (x + 7)(x + 3)
Answer:
(b) (x + 7)(x − 3)
Page No 104:
Question 15:
Tick (✓) the correct answer:
y2 + 2y − 3 = ?
(a) (y − 1)(y + 3)
(b) (y + 1)(y − 3)
(c) (y − 1)(y − 3)
(d) (y + 2)(y − 3)
Answer:
(a) (y − 1)(y + 3)
Page No 104:
Question 16:
Tick (✓) the correct answer:
40 + 3x − x2 = ?
(a) (x + 5)(x − 8)
(b) (5 − x)(8 + x)
(c) (5 + x)(8 − x)
(d) (5 − x)(8 − x)
Answer:
(c) (5 + x)(8 − x)
Page No 104:
Question 17:
Tick (✓) the correct answer:
2x2 + 5x + 3 = ?
(a) (x + 3)(2x + 1)
(b) (x + 1)(2x + 3)
(c) (2x + 5)(x − 3)
(d) none of these
Answer:
(b) (x + 1)(2x + 3)
Page No 104:
Question 18:
Tick (✓) the correct answer:
6a2 − 13a + 6 = ?
(a) (2a + 3)(3a − 2)
(b) (2a − 3)(3a + 2)
(c) (3a − 2)(2a − 3)
(d) (3a + 1)(2a − 3)
Answer:
(c) (3a − 2)(2a − 3)
Page No 104:
Question 19:
Tick (✓) the correct answer:
4z2 − 8z + 3 = ?
(a) (2z − 1)(2z − 3)
(b) (2z + 1)(3 − 2z)
(c) (2z + 3)(3z − 1)
(c) (z − 1)(4z − 3)
Answer:
(a) (2z − 1)(2z − 3)
Page No 104:
Question 20:
Tick (✓) the correct answer:
3 + 23y − 8y2 = ?
(a) (1 − 8y)(3 + y)
(b) (1 + 8y)(3 − y)
(c) (1 − 8y)(y − 3)
(d) (8y − 1)(y + 3)
Answer:
(b) (1 + 8y)(3 − y)
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