M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 4 factorization

Exercises in Chapter 4 factorization Grade 9

Factorization Exercise 4.1

Factorization Exercise 4.2

Factorization Exercise 4.3

Factorization Exercise 4.4

Factorization Exercise 4.5

Questions in Factorization Exercise 4.1

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

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

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

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

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

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

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

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

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

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

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

Questions in Factorization Exercise 4.2

$4 x^{2}-25 y^{2}$

$\text { (ii) } 9 x^{2}-1$

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

$\text { (ii) } 9(x+y)^{2}-x^{2}$

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

$\text { (ii) } 9 x^{2}-4(y+2 x)^{2}$

$(i) 2(x-2 y)^{2}-50 y^{2}$

$\text { (ii) } 32-2(x-4)^{2}$

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

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

(i) a(a - 2) – b(b - 2)

(ii) a(a - 1) – b(b - 1)

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

$\text { (ii) } x^{3}-25 x$

$\text { (i) } 2 x^{4}-32$

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

$(i)\left(a^{2}-b^{2}\right)\left(c^{2}-d^{2}\right)-4 a b c d$

$(i i) 4 x^{2}-y^{2}-3 x y+2 x-2 y$

$(i) a^{4}+b^{4}-7 a^{2} b^{2}$

$\text { (ii) } x^{4}-14 x^{2}+1$

$(i)\left(x^{2}-5 x+7\right)\left(x^{2}+5 x+7\right)$

$(\mathrm{ii})\left(\mathrm{x}^{2}-5 \mathrm{x}+7\right)\left(\mathrm{x}^{2}-5 \mathrm{x}-7\right)$

$(\text { iii) })\left(x^{2}+5 x-7\right)\left(x^{2}-5 x+7\right)$

$\text { (i) } x-1 / x=5 / 6$

$(\mathrm{ii})(\mathrm{x}+1 / \mathrm{x})^{2}=\left(\mathrm{x}^{2}+\left(1 / \mathrm{x}^{2}\right)+2\right)$

$\text { (iii) }(x+1 / x)^{3}=x^{3}+\left(1 / x^{3}\right)+3(x+(1 / x))$

$\text { (iv) } x^{4}-1 / x^{4}$

If x + 1/x = √3, find the values of

$\text { (i) } x^{3}+1 / x^{3}$

$\text { (ii) } x^{6}-1 / x^{6}$

Questions in Factorization Exercise 4.3

$(i) x^{2}+6 x-7$

$\text { (ii) } y^{2}+7 y-18$

$(i) y^{2}-7 y-18$

$\text { (ii) } a^{2}-3 a-54$

$(i) 2 x^{2}-7 x+6$

$\text { (ii) } 6 x^{2}+13 x-5$

$\text { (i) } 2 x^{2}-x-6$

$\text { (ii) } 1-18 y-63 y^{2}$

(i) x(12x + 7) – 10

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

$\text { (i) } 60 x^{2}-70 x-30$

$\text { (ii) } x^{2}-6 x y-7 y^{2}$

$\text { (i) } 2 x^{2}+13 x y-24 y^{2}$

$\text { (ii) } 6 x^{2}-5 x y-6 y^{2}$

$(i) 2 a^{2} b^{2}-7 a b-30$

$\text { (ii) } a(2 a-b)-b^{2}$

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

$(2 x-y)^{2}-11(2 x-y)+28$

$(\mathrm{i}) 4(\mathrm{a}-1)^{2}-4(\mathrm{a}-1)-3$

$\text { (ii) } 1-2 a-2 b-3(a+b)^{2}$

$4(2 a-3)^{2}-3(2 a-3)(a-1)-7(a-1)^{2}$

$\left(2 x^{2}+5 x\right)\left(2 x^{2}+5 x-19\right)+84$

Questions in Factorization Exercise 4.4

$\text { (i) } 25 a b c^{2}-15 a^{2} b^{2} c$

$\text { (ii) } 28 p^{2} q^{2} r-42 p q^{2} r^{2}$

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

(ii) 14mn + 22m – 62p

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

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

Questions in Factorization Exercise 4.5

$\text { (i) } 64 x^{3}+1$

$(\text { ii }) 7 a^{3}+56 b^{3}$

$(i) 27 x^{3} y^{3}-8$

$\text { (ii) } 27(x+y)^{3}+8(2 x-y)^{3}$

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

$\text { (ii) } a^{3}-b^{3}-a+b$

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

$\text { (ii) } a^{3}-a-120$

$\text { i) } x^{3}+6 x^{2}+12 x+16$

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

$\text { (i) } 2 a^{3}+16 b^{3}-5 a-10 b$

$(\mathrm{ii}) \mathrm{a}^{3}-\left(1 / \mathrm{a}^{3}\right)-2 \mathrm{a}+2 / \mathrm{a}$

$(\mathrm{i}) \mathrm{a}^{6}-\mathrm{b}^{6}$

$\text { (ii) } x^{6}-1$

$\text { (i) } 64 x^{6}-729 y^{6}$

$\text { (ii) } x^{3}-(8 / x)$

$\text { (i) } 250(a-b)^{3}+2$

$\text { (ii) } 32 a^{2} x^{3}-8 b^{2} x^{3}-4 a^{2} y^{3}+b^{2} y^{3}$

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

$\text { (ii) } x^{6}-7 x^{3}-8$

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Chapters in this book

Rational and Irrational Numbers

Compound Interest

Expansions

Factorization

Simultaneous Linear Equations

Problems on Simultaneous Linear Equations

Quadratic Equations

Indices

Logarithms

Triangles

Mid Point Theorem

Pythagoras Theorem

Rectilinear Figures

Theorems on Area

Circle

Mensuration

Trigonometric Ratios

Trigonometric Ratios and Standard Angles

Coordinate Geometry

Statistics