Worksheet on Factorization 1
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Here ask-math has given you worksheet on factorization 1 :Q.1 Using a suitable identity, find the following products :
a) (x + 5)(x – 3)
b) (4x + 3)(4x + 5)
c) (x + y)(x + y)
e) (3x + 4)(3x + 7)
f) (5a + 3)(5a + 2)
Q.2 Expand using suitable formula :
a) (2a + 3) 2
b) (3a – 5) 2
Q.3 Factorise the following :
a) x 2 + 6x + 9
b) 24x 2 – 41x + 12
c) x 2 – x – 6
d) 16x 2 + 8x + 1
e) 9x 2 – 16y 2
f) 4x 3 – 4x
g) (x + 1) 2 – (x – 1) 2
h) 9x 2 + 6x + 1 – 25y 2
i) 25x 2 – 10x + 1 – 36y 2
j) x 3 + x – 3x 2 – 3
k) x 2 + y – xy – x
l) 3ax – 6ay – 8by + 4bx
m) xy – ab + bx – ay
n) 1 – x 2 – y 2 – 2xy
o) 8 – 4a – 2a 3 + a 4
p) a 2 + b 2 + 2ab + 2bc + 2ca
q) x 3 + 64
r) 25x 2 – 10x + 1
s) x 2 – 11x – 42
t) 12x 2 – 10x + 2
u) a 4 – a
v) x 3 – 125
w)27x 3 y 3 – 8z 3
x) 8x 3 – (2x – y) 3
y) (a + b) 3 – (a – b) 3
Q.4 Factorise the following :
i) 4(x – y) 2 – 12(x – y)(x + y) + 9(x + y) 2
ii) 3(x + y) 2 – 5(x + y ) + 2
iii) 12(x 2 + 7x) 2 – 8(x 2 + 7x)(2x – 1) – 15(2x – 1) 2
iv) x 2 – 5x + 6
v)4x 2 + 9y 2 + z 2 + 12xy + 4xz + 6yz
vi) x 3 – x 2 y + xy 2 – y 3
vii) a 3 +a 2 b +ab 2 + b 3
Q.5 Solve using appropriate formula :
i) (2a + 3)(2a – 3)
ii) (105) 2
iii)(49) 2
iv) (536) 2 – (136) 2
v) if 4x = 7 2 – 3 2 , then find the value of x.
vi) 998 × 1002
Q.6 Simplify :
(a + b) 3 + (a – b) 3 + 6a(a 2 – b 2 ).
Q.7. Show that if 2(a 2 + b 2 ) = (a + b) 2 , then a = b.
Q.8 Expand each of the following :
i) (x + 2y) 3
ii) (2x – 3y) 3
iii) (x 2 + 2y) 3
Q.9 Evaluate the following using suitable identities :
i) (98) 3
ii) (101) 3
iii) (999) 3
Q.10 Show that if (a + b) is not zero, then the equation :
a(x – a) = 2ab – b(x – b) has a solution x = a + b.
Q.11 Foctorise each of the following :
i) a 4 – b 4
ii) a 4 – 16b 4
iii) a 2 – (b – c) 2
iv) x 2 + 7xy + 12y 2
v) x 2 + 2ax – b 2 – 2ab
vi) (x 2 + x) 2 + 4(x 2 + x) – 12
vii) 5x 2 + 16x + 3.
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