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

Exercises in Chapter 5 chapter 5 factorisation Grade 9

Exercise 5(A)

Exercise 5(B)

Exercise 5(C)

Exercise 5(D)

Exercise 5(E)

Questions in Exercise 5(A)

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

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:

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

Questions in Exercise 5(B)

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:

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

Questions in Exercise 5(C)

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:

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

Questions in Exercise 5(D)

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 )

Questions in Exercise 5(E)

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:

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

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

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

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

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Chapters in this book

Chapter 1- Rational and Irrational Numbers

Chapter 2- Compound Interest [Without Using Formula

Chapter 3- Compound Interest [Using Formula

Chapter 4- Expansions

Chapter 5- Factorisation

Chapter 6- Simultaneous Equations

Chapter 7- Indices [exponents]

Chapter 8- Logarithms

Chapter 9- Triangles [Congruency in Triangles]

Chapter 10- Isosceles Triangle

Chapter 11- Inequalities

Chapter 12- Mid-Point and Its Converse

Chapter 13- Pythagoras Theorem

Chapter 14- Rectilinear Figures

Chapter 15- Construction of Polygons

Chapter 16- Area Theorems

Chapter 17- Circles

Chapter 18- Statistics

Chapter 19- Mean and Median

Chapter 20- Area and Perimeter of Plane Figures

Chapter 21- Solids

Chapter 22- Trigonometrical Ratios

Chapter 23- Trigonometrical Ratios of Standard Angles

Chapter 24- Solution Of Right Triangles

Chapter 25- Complementary angles

Chapter 26- Co-ordinate Geometry

Chapter 27- Graphical Solution

Chapter 28- Distance Formula

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