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

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)

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}

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}

(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}

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)