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) x² + 6x + 9
b) 24x² – 41x + 12
c) x² – x – 6
d) 16x² + 8x + 1
e) 9x² – 16y²
f) 4x³ – 4x
g) (x + 1) ² – (x – 1) ²
h) 9x² + 6x + 1 – 25y²
i) 25x² – 10x + 1 – 36y²
j) x³ + x – 3x² – 3
k) x² + y – xy – x
l) 3ax – 6ay – 8by + 4bx
m) xy – ab + bx – ay
n) 1 – x² – y² – 2xy
o) 8 – 4a – 2a³ + a⁴
p) a² + b² + 2ab + 2bc + 2ca
q) x³ + 64
r) 25x² – 10x + 1
s) x² – 11x – 42
t) 12x² – 10x + 2
u) a⁴ – a
v) x³– 125
w)27x³y³ – 8z³
x) 8x³ – (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(x² + 7x) ² – 8(x² + 7x)(2x – 1) – 15(2x – 1) ²
iv) x² – 5x + 6
v)4x² + 9y² + z² + 12xy + 4xz + 6yz
vi) x³ – x²y + xy² – y³
vii) a³ +a²b +ab² + b³
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 = 7² – 3², then find the value of x.
vi) 998 × 1002
Q.6 Simplify :
(a + b) ³ + (a – b) ³ + 6a(a² – b²).
Q.7. Show that if 2(a² + b²) = (a + b) ², then a = b.
Q.8 Expand each of the following :
i) (x + 2y) ³
ii) (2x – 3y) ³
iii) (x²+ 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) a⁴ – b⁴
ii) a⁴ – 16b⁴
iii) a² – (b – c) ²
iv) x² + 7xy + 12y²
v) x² + 2ax – b²– 2ab
vi) (x² + x) ² + 4(x² + x) – 12
vii) 5x² + 16x + 3.

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worksheet on factorization 1

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