M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 11 factorisation

Exercises in Chapter 11 factorisation Grade 8

Factorisation Exercise 11.1

Factorisation Exercise 11.2

Factorisation Exercise 11.3

Factorisation Exercise 11.4

Factorisation Exercise 11.5

Questions in Factorisation Exercise 11.1

Factorise the following polynomials:

$(i) 8 x y^{3}+12 x^{2} y^{2} (ii) 15 a x^{3}-9 a x^{2}$

$(i) 21 py ^{2}-56 p y (ii) 4 x^{3}-6 x^{2}$

$(i) 25 a b c^{2}-15 a^{2} b^{2} c (ii) x^{2} y z+x y^{2} z+x y z^{2}$

$(i) 8 x^{3}-6 x^{2}+10 x$

$(ii) 14 \mathrm{mn}+22 \mathrm{m}-62 \mathrm{p}$

$(i) 18 p^{2} q^{2}-24 p q^{2}+30 p^{2} q$

$(ii) 27 a^{3} b^{3}-18 a^{2} b^{3}+75 a^{3} b^{2}$

$(i) 15 a(2 p-3 p)-106(2 p-3 q)$

$(ii) 3 a\left(x^{2}+y^{2}\right)+6 b\left(x^{2}+y^{2}\right)$

$(i) 6(x+2 y)^{3}+8(x+2 y)^{2}$

$(ii) 14(a-3 b)^{3}-21 p(a-3 b)$

$10 a(2 p+q)^{3}-15 b(2 p+q)^{2}+35(2 p+q)$

Questions in Factorisation Exercise 11.2

Factorise the following polynomials:

$(i) x^{2}+x y-x-y$

$(ii) y^{2}-y z-5 y+5 z$

$(i) 5 x y+7 y-5 y^{2}-7 x$

$(ii) 5 p^{2}-8 p q-10 p+16 q$

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

$(ii) x^{3}-3 x^{2}+x-3$

$(i) 6 x y^{2}-3 x y-10 y+5$

$(ii) 3 a x-6 a y-8 b y+4 b x$

$(i) x^{2}+x y(1+y)+y^{3}$

$(ii) y^{2}-x y(1-x)-x^{3}$

$(i) a b^{2}+(a-1) b-1$

$(ii) 2 a-4 b-x a+2 b x$

$(i) 5 p h-10 q k+2 r p h-4 q r k$

$(ii) x^{2}-x(a+2 b)+2 a^{2}$

$(i) ab \left(x^{2}+y^{2}\right)-x y\left(a^{2}+b^{2}\right)$

$(ii) (\mathbf{a x}+\mathbf{b y})^{2}+(\mathbf{b x}-\mathbf{a y})^{2}$

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

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

$(i) a^{2} b+a b^{2}-a b c-b^{2} c+a x y+b x y$

$(ii) a x^{2}-b x^{2}+a y^{2}-b y^{2}+a z^{2}-b z^{2}$

$(i) x-1-(x-1)^{2}+a x-a$

$(ii) a x+a^{2} x+a b y+b y-(a x+b y)^{2}$

Questions in Factorisation Exercise 11.3

Factorise the following expressions using algebraic identities:

$(i) x^{2}-12 x+36 (ii) 36 p^{2}-60 p q+25 q^{2} (iii) 9 y^{2}+66 x y+121 y^{2} (iv) a^{4}+6 a^{2} b^{2}+9 b^{4} (v) x^{2}+1 / x^{2}+2 (vi) x^{2}+x+1 / 4$

Factorise the following expressions:

$(i) 4 p^{2}-9$

$(ii) 4 x^{2}-169 y^{2}$

$(i) 9 x^{2} y^{2}-25$

$(ii) 16 x^{2}-1 / 144$

$(i) 20 x^{2}-45 y^{2}$

$(ii) 9 / 16-25 a^{2} b^{2}$

$(i) (2 a+3 b)^{2}-16 c^{2}$

$(ii) 1-(b-c)^{2}$

$(i) 9(x+y)^{2}-x^{2}$

$(ii) (2 m+3 n)^{2}-(3 m+2 n)^{2}$

$(i) 25(a+b)^{2}-16(a-b)^{2}$

$(ii) 9(3 x+2)^{2}-4(2 x-1)^{2}$

$(i) x^{3}-25 x$

$(ii) 63 p^{2} q^{2}-7$

$(i) 32 a^{2} b-72 b^{3}$

$(ii) 9(a+b)^{3}-25(a+b)$

$(i) x^{2}-y^{2}-2 y-1$

$(ii) p^{2}-4 p q+4 q^{2}-r^{2}$

$(i) 9 x^{2}-y^{2}+4 y-4$

$(ii) 4 a^{2}-4 b^{2}+4 a+1$

$(i) 625-p^{4}$

$(ii) 5 y^{5}-405 y$

$(i) x^{4}-y^{4}+x^{2}-y^{2}$

$(ii) 64 a^{2}-9 b^{2}+42 b c-49 c^{2}$

Questions in Factorisation Exercise 11.4

$(i) x^{2}+3 x+2$

$(ii) z^{2}+10 z+24$

$(i) y^{2}-7 y+12$

$(ii) m^{2}-23 m+42$

$(i) y^{2}-5 y-24$

$(ii) t^{2}+23 t-108$

$(i) 3 x^{2}+14 x+8$

$(ii) 3 y^{2}+10 y+8$

$(i) 14 x^{2}-23 x+8$

$(ii) 12 x^{2}-x-35$

$(i) 6 x^{2}+11 x-10$

$(ii) 5-4 x-12 x^{2}$

$(i) 1-18 y-63 y^{2}$

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

$(i) x^{2}-3 x y-40 y^{2}$

$(ii) 10 p^{2} q^{2}-21 p q+9$

$(i) 2 a^{2} b^{2}+a b-45$

$(ii) x(12 x+7)-10$

$(i) (a+b)^{2}-11(a+b)-42$

$(ii) 8+6(p+q)-5(p+q)$

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

$(ii) 7+10(2 x-3 y)-8(2 x-3 y)^{2}$

Questions in Factorisation Exercise 11.5

Work out the following divisions:

$(\mathbf{i})(\mathbf{3 5} \mathbf{x}+\mathbf{2 8}) \div(\mathbf{5} \mathbf{x}+\mathbf{4})$

$(ii) 7 p^{2} q^{2}(9 r-27) \div 63 p q(r-3)$

Divide as directed: $(i) 6(2 x+7)(5 x-3) \div 3(5 x-3)$

$(ii) 33 p q(p+3)(2 q-5) \div 11 p(2 q-5)$

Factorise the expression and divide them as directed:

$(i) \left(7 x^{2}-63 x\right) \div 7(x-3)$

$(ii) \left(3 p^{2}+17 p+10\right) \div(p+5)$

$(iii) 10 x y\left(14 y^{2}+43 y-21\right) \div 5 x(7 y-3)$

$(iv) 12 p q r\left(6 p^{2}-13 p q+6 q^{2}\right) \div 6 p q(2 p-3 q)$

Find the HCF of the given polynomials: $(i) 14 \mathrm{pq}, 28 \mathrm{p}^{2} \mathrm{q}^{2}$

$(ii) 8 a b c, 24 a b^{2}, 12 a^{2} b$

Factorise the following: $(i) 10 x^{2}-18 x^{3}+14 x^{4}$

$(ii) 5 x^{2} y+10 x y z+15 x$

$(iii) p^{2} x^{2}+c^{2} x^{2}-a c^{2}- ap^{2}$

$(iv) 15(x+y)^{2}-5 x-5 y$

$(\mathbf{v})(\mathbf{a} \mathbf{x}+\mathbf{b} \mathbf{y})^{2}+(\mathbf{a} \mathbf{y}-\mathbf{b} \mathbf{x})^{2}$

$(v i) a x+b y+c x+b x+c y+a y$

$(vii) 49 x^{2}-70 x y+25 y^{2}$

$(viii) 4 a^{2}+12 a b+9 b^{2}$

$(ix) 49 p^{2}-36 q^{2}$

$(x) 100 x^{3}-25 x y^{2}$

$(xi) x^{2}-2 x y+y^{2}-z^{2}$

$(xii) x^{8}-y^{8}$

$(xiii) 12 x^{3}-14 x^{2}-10 x$

$(xiv) p^{2}-10 p+21$

$(xv) 2 x^{2}-x-6$

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

$(xvii) x^{2}+2 x y-99 y^{2}$

Divide as directed:

$(i) 15(y+3)\left(y^{2}-16\right) \div 5\left(y^{2}-y-12\right)$

$(ii) \left(3 x^{3}-6 x^{2}-24 x\right) \div(x-4)(x+2)$

$(iii) \left(x^{4}-81\right) \div\left(x^{3}+3 x^{2}+9 x+27\right)$

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Chapters in this book

Rational Numbers

Exponents and Powers

Squares and Square Roots

Cubes and Cube Roots

Playing with Numbers

Operation on sets Venn Diagrams

Percentage

Simple and Compound Interest

Direct and Inverse Variation

Algebraic Expressions and Identities

Factorisation

Linear Equations and Inequalities In one Variable

Understanding Quadrilaterals

Constructions of Quadrilaterals

Circle

Symmetry Reflection and Rotation

Visualising Solid Shapes

Mensuration

Data Handling