Factorisation Class 8 Worksheet with Answers
1. Factorise
the following expressions.
a. 8a – 24
b. 5x2
+ 25x
c. 9p2 + 15q2
d.
–35yz + 21z2
e. xy + yz + xyz
f.
3x – 9a
g. 5x3 – 15x
h. 26xy3
– 13x3y2 + 52xy2
2. Factorise
each of the following:
a. ax – b + ab – x
b. x + 6y
– 6 – xy
c. 3y2 + y3 + 3 + y
d. 9xy + 6yz +
15px + 10zp
e. ax + ay + bx + by
f. 15xy – 6x + 5y
– 2
3. Factorise
each of the following:
a. 9x2(1 – y)
+ 6x(1 – y) – 12(1 – y)
b. 3yz(a – b – c)
– 3z(a – b – c) + 21z2(a –
b – c)
c. 15x(lu – mv) +
25y(lu – mv) + 30z (lu – mv)
d. 20(p2 – q2)2
– 30(p2 – q2)3 + 5(p2
– q2)
4. Factorise
the following.
a. 9x2 – 12xy + 4y2
b. 25a2
+ 60ab + 36b2
c. 49p2 – 112pq + 64q2
d. 81a2 + 72ab + 16b2
e. a4 – 2a2b2 + b4
f. 4x2 + 12xy + 9y2
5. Factorise the following expressions by grouping:
a. xy + 4x + 2y + 8
b. ab – 3a +
2b – 6
c. ac – ad + bc – bd
d. 6 + 2y + 3x + xy
e. ab – ad – bc + cd
f.
a – ab + b – b2
g. 4p – 6q – 6p2 + 9pq
h.
2x – xy + 4y – 8
i. 3x – xy + 4y – 12
j. 5p – pq + 2q – 10
k. 6 – 2y + xy – 3x
l. 7(x
+ y) – 14x – 14y
6. Factorise the following:
a. 4x2 – 9
b.
25x2 – 16
c. 49x2 – 81
d. 25y4 – 16
e. 64x2 – 36
f. 16x8
– 625
g. (5p + 7q)2 – (7p + 5q)2
h. 28x3 – 7x
7. Factorise the following:
a. x2 – 14x + 45
b. x2
+ 18x + 81
c. x2 – 8x + 16
d. x2
+ 11x – 42
e. x2 + 16x – 80
f. x2
+ 16x + 48
g. 2x2 + 5x – 12
h. 7x2
– 5x – 12
i. 5x2 + x – 18
j. x2 – 6x – 40
ANSWERS
1. a. 8(a – 3)
b. 5x(x + 5)
c. 3(3p2 + 5q2)
d. 7z(–5y + 3z)
e. y(x + z + xz)
f. 3(x – 3a)
g. 5x(5x2
– 3)
h. 13xy2(2y
– x2 + 4)
2. a. (a – 1) (x +
b)
b. (1 – y) (x – 6)
c. (y2 + 1) (y + 3)
d. (3x + 2z) (3y +
5p)
e. (x + y) (a + b)
f.
(5y – 2) (3x + 1)
3. a. 3(1 – y) (3x2
+ 2x – 4)
b. 3z(a – b – c) (y – 1 + 7z)
c. 5(lu – mv) (3x + 5y + 6z)
d. 5(p2 – q2) [4(p2
– q2) – 6(p2 – q2)2
+ 1]
4. a. (3x
– 2y)2
b. (5a + 6b)2
c. (7p – 8q)2
d. (9a + 4b)2
e. (a2 – b2)2
f. (2x + 3y)2
5. a. (x
+ 2) (y + 4)
b. (a + 2) (b – 3)
c. (a + b) (c – d)
d. (2 + x) (3 + y)
e. (a – c) (b – d)
f. (1 – b) (a + b)
g. (2p – 3q) (2 – 3p)
h. (2 – y) (x – 4)
i. (3 – y) (x – 4)
j. (5 – q) (p – 2)
k. (3 – y) (2 – x)
l. -7(x + y)
6. a. (2x
+ 3) (2x – 3)
b. (5x + 4) (5x – 4)
c. (7x + 9) (7x – 9)
d. (5y2 + 4) (5y2
– 4)
e. 4(4x + 3) (4x – 3)
f. (4x4 + 25) (4x4
– 25)
g. 24(p + q) (q – p)
h. 7x(2x + 1) (2x – 1)
7. a. (x
– 9) (x – 5)
b. (x + 9) (x + 9)
c. (x – 4) (x – 4)
d. (x + 14) (x – 3)
e. (x + 20) (x – 4)
f. (x + 12) (x + 4)
g. (x + 4) (2x – 3)
h. (x + 1) (7x – 12)
i. (x + 2) (5x – 9)
j. (x + 4) (x – 10)
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