Selina solutions concise maths class 9 icse Solutions for Chapter 5 chapter 5 factorisation

x y\left(3 x^{2}-2 y^{2}\right)-y z\left(2 y^{2}-3 x^{2}\right)+z x\left(15 x^{2}-10 y^{2}\right)

Factorise by grouping method:

16(a+b)^{2}-4 a-4 b

Factorise by grouping method:

a b-2 b+a^{2}-2 a

Factorise by grouping method:

a^{2}+b-a b-a

Factorise by grouping method:

(2 a-b)^{2}-10 a+5 b

Factorise by grouping method:

a(a-4)-a+4

Factorise by grouping method:

y^{2}-(a+b) y+a b

Factorise by grouping method:

x(6 x-5 y)-4(6 x-5 y)^{2}

Factorise:

a^{2}+10 a+24

Factorise:

1-2 a-3 a^{2}

Factorise:

x^{2}-3 a x-88 a^{2}

Factorise:

6 a^{2}-a-15

Factorise:

a(3 a-2)-1

Factorise:

(2 a+b)^{2}-6 a-3 b-4

Factorise:

1-2(a+b)-3(a+b)^{2}

Factorise:

x^{2}+3 x+2+a x+2 a

Factorise:

\frac{1}{35}+\frac{12}{35} a+a^{2}

Factorise:

\left(x^{2}-3 x\right)\left(x^{2}-3 x-1\right)-20

For each trinomial (quadratic expression), given below, find whether it is factorisable or not.

Factorise, if possible.

\begin{aligned} &\text { (i) }\\ &x;^{2}-3 x-54 \end{aligned} \begin{aligned} &\text { (ii) }\\ &2 x^{2}-7 x-15 \end{aligned} \begin{aligned} &\text { (iii) }\\ &2 x^{2}+2 x-75 \end{aligned}

\begin{aligned} &\text { (iv) }\\ &3 x^{2}+4 x-10 \end{aligned}

\begin{aligned} &(\mathrm{v})\\ &x;(2 x-1)-1 \end{aligned}

Factorise:

\begin{aligned} &\text { (i) }\\ &4 \sqrt{3} x^{2}+5 x-2 \sqrt{3} \end{aligned}\begin{aligned} &\text { (ii) }\\ &7 \sqrt{2} x^{2}-10 x-4 \sqrt{2} \end{aligned}

Factorise:

a^{2}-(2 a+3 b)^{2}

Factorise:

25(2 a-b)^{2}-81 b^{2}

Factorise:

3 a^{5}-108 a^{3}

Factorise:

9(a-2)^{2}-16(a+2)^{2}

Factorise:

a^{4}-1

Factorise:

(a+b)^{3}-a-b

Factorise:

4 a^{2}-\left(4 b^{2}+4 b c+c^{2}\right)

Factorise:

9 a^{2}+3 a-8 b-64 b^{2}

Factorise:

4 x^{2}-12 a x-v^{2}-z^{2}-2 v z+9 a^{2}

Factorise:

x^{4}+x^{2}+1

Factorise:

\left(a^{2}+b^{2}-4 c^{2}\right)^{2}-4 a^{2} b^{2}

Factorise:

\left(x^{2}+4 y^{2}-9 z^{2}\right)^{2}-16 x^{2} y^{2}

Factorise:

(a+b)^{2}-a^{2}+b^{2}

Factorise:

a^{2}-b^{2}-(a+b)^{2}

Factorise:

9 a^{2}-\left(a^{2}-4\right)^{2}

Factorise:

4 x^{2}+\frac{1}{4 x^{2}}+1

Factorise:

4 x^{4}-x^{2}-12 x-36

Factorise:

a^{3}-27

Factorise:

1-3 a^{3}

Factorise:

a^{6}+27b^{3}

Factorise:

a^{3}-\frac{27}{a^{3}}

Factorise:

a^{3}+0.064

Factorise:

\frac{8 a^{3}}{27}-\frac{b^{3}}{8}

Factorise:

a^{6}-7 a^{3}-8

Factorise:

8 a^{3}-b^{3}-4 a x+2 b x

Factorise:

a-b-a^{3}+b^{3}

Factorise:

2 x^{3}+54 y^{3}-4 x-12 y

Show that:

(i) (13³ – 5³) is divisible by 8.

(ii) (35³ + 27³ )

Factorise:

x^{2}+\frac{1}{4 x^{2}}+1-7 x-\frac{7}{2 x}

Factorise:

9 a^{2}+\frac{1}{9 a^{2}}-2-12 a+\frac{4}{3 a}

Factorise:

x^{2}+\frac{a^{2}+1}{a} x+1

Factorise:

x^{4}+y^{4}-27 x^{2} y^{2}

Factorise:

4 x^{4}+9 y^{4}+11 x^{2} y^{2}

Factorise:

x^{2}+\frac{1}{x^{2}}-3

Factorise:

a-b-4 a^{2}+4 b^{2}

Factorise:

(2 a-3)^{2}-2(2 a-3)(a-1)+(a-1)^{2}

Factorise:

\left(a^{2}-a\right)\left(4 a^{2}-4 a-5\right)-6

Factorise:

x^{4}+y^{4}-3 x^{2} y^{2}

Factorise:

5 a^{2}-b^{2}-4 a b+7 a-7 b

Factorise:

12(3 x-2 y)^{2}-3 x+2 y-1

Factorise:

4(2 x-3 y)^{2}-8 x+12 y-3

Factorise:

3-5 x+5 y-12(x-y)^{2}

Factorise:

9 x^{2}+3 x-8 y-64 y^{2}

Factorise:

2 \sqrt{3} x^{2}+x-5 \sqrt{3}

Find the value of:

\text { (i) }(987)^{2}-(13)^{2}

\text { (ii) }(67.8)^{2}-(32.2)^{2}

\text { (iii) } \frac{(6.7)^{2}-(3.3)^{2}}{6.7-3.3}

\text { (iv) } \frac{(18.5)^{2}-(6.5)^{2}}{4^{-}}