Ncert solutions mathematics class 8 Solutions for Chapter 14 factorisation

Exercises in Chapter 14 factorisation Grade 8

Exercise 14.1

Exercise 14.2

Exercise 14.3

Exercise 14.4

Questions in Exercise 14.1

Q1) Find the common factors of the given terms.

(i) 12x, 36

(ii) 2y, 22xy

(iii) $14\ pq,\ 28p^2q^2$

(iv) $2x,3x^2,\ 4$

(v) $6abc,\ 24ab^2,\ 12a^2b$

(vi) $16x^3,\ -4x^2,\ 32x$

(vii) $10\ pq,\ 20qr,\ 30rp$

(viii) $3x^2y^3,\ 10x^3y^2,\ 6x^2y^2z$

Find the common factors of the given terms.

Q2) Factorise the following expressions.

(i) 7x – 42

(ii) 6p – 12q

(iii) $7a^2+14a\$

(iv) $-16z\ +20z^3$

(v) $20l^2m+30alm$

(vi) $5x^2y\ -\ 15xy^2$

(vii) $10a^2-15b^2+20c^2$

(viii) $-4a^2+4ab-4ca$

(ix) $x^2yz+xy^2z+xyz^2$

(x) $ax^2y+bxy^2+cxyz$

Factorize the following expressions

Factorise:

(i) x^2 + x y + 8x + 8y

(ii) 15 xy – 6x + 5y – 2

(iii) ax + bx – ay – by

(iv) 15 pq + 15 + 9q + 25p

(v) z – 7 + 7 x y – x y z

Q3) Factorize :

(i) $x^2+xy+8x+8y$

(ii) 15xy-6x+5y-2

(iii) ax+bx-ay-by

(iv) 15pq+15+9q+25p

(v) z-7+7xy-xyz

Q21) $\frac{7x+5}{5}=7x$

Questions in Exercise 14.2

Factorise the expression:

$p^{2}-10 p+25$

Factorise the expression:

$49 y^{2}+84 y z+36 z^{2}$

Factorise the expression:

$121 b^{2}-88 b c+16 c^{2}$

Factorise the expression:

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

Q1) Factorise the following expressions.

(i) $a^2+8a+16$

(ii) $p^2-10p+25$

(iii) $25m^2+30m+9$

(iv) $49y^2+84yz+36z^2$

(v) $4x^2-8x+4$

(vi) $121b^2\ -\ 88bc\ +16c^2$

(vii) $\left(l+m\right)^2-4lm$

(viii) $25a^2-4b^2+28bc-49c^2$

Factorise the expression:

$(1+m)^{2}-4 ! m\left(\text { Hint: Expand }(1+m)^{2} \text { first }\right)$

Factorise the expression:

$a^2 + 8a + 16$

Factorise the expression:

25 m^{2}+30 m+9

Factorise:

$25 a^{2}-4 b^{2}+28 b c-49 c^{2}$

Factorise:

$(1+m)^{2}-(1-m)^{2}$

Factorise:

$9 x^{2} y^{2}-16$

Factorise:

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

Factorise:

$49 x^{2}-36$

Q2) Factorise.

(i) $4p^2-9q^2$

(ii) $63a^2-112b^2$

(iii) $49x^2-36$

(iv) $16x^5-144x^3$

(v) $\left(l+m\right)^2-\left(l-m\right)^2$

(vi) $9x^2y^2-16$

(vii)

Factorise:

$63 a^{2}-112 b^{2}$

Factorise:

$16 x^{5}-144 x^{3}$

Factorise:

$4 p^{2}-9 q^{2}$

Factorize the expressions.

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

(ii) $7 p^{2}+21 q^{2}$

(iii) $2 x^{3}+2 x y^{2}+2 x z^{2}$

(iv) $a m^{2}+b m^{2}+b n^{2}+a n^{2}$

(v) $(\ln +1)+m+1$

(vi) $y(y+z)+9(y+z)$

(vii) $5 y^{2}-20 y-8 z+2 y z$

(viii) $10 a b+4 a+5 b+2$

(ix) 6xy – 4y + 6 – 9x

Q3) Factorise the expressions:

(i) $ax^2+bx$

(ii) $7p^2+21q^2$

(iii) $2x^3+2xy^2+2xz^2$

(iv) $am^2+bm^2+bn^2+an^2$

(v) (lm+1)+m+1

(vi) y(y+z)+9(y+z)

(vii) $5y^2-20y-8z+2yz$

(viii) 10ab+4a+5b+2

(ix)6xy-4y+6-9x

Factorise:

$a^{4}-b^{4}$

Q4) Factorise:

(i) $a^4-b^4$

(ii) $p^4-81$

(iii) $x^4-\left(y+z\right)^4$

(iv) $x^4-\left(x-z\right)^4$

(v) $a^4-2a^2b^2+b^4$

Factorise:

$p^{4}-81$

Factorise:

$x^{4}-(y+z)^{4}=\left(x^{2}\right)^{2}-\left[(y+z)^{2}\right]^{\wedge} 2$

Factorise:

$x^{4}-(x-z)^{4}=\left(x^{2}\right)^{2}-\left\{(x-2)^{2}\right\}^{2}$

Factorise:

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

Factorise:

$q^{2}-10 q+121$

Q5)Factorise the following expressions:

(i) $p^2+6p+8$

(ii) $q^2-10q+21$

(iii) $p^2+6p-16$

Factorise the expression:

$4 x^{2}-8 x+4$

Factorise the expression:

$p^{2}+6 p+8$

Factorise:

$p^{2}+6 p-16$

Questions in Exercise 14.3

Carry out the following divisions:

$\text { (i) } 28 x^{4} \div 56 x$

$\text { (ii) }-36 y^{3} \div 9 y^{2}$

$\text { (iii) } 66 \mathrm{pq}^{2} \mathrm{r}^{3} \div 11 \mathrm{qr}^{2}$

$\text { (iv) } 34 x^{3} y^{3} z^{3} \div 51 x y^{2} z^{3}$

$\text { (v) } 12 a^{8} b^{8} \div\left(-6 a^{6} b^{4}\right)$

Q1) Carry out the following divisions:

(i) $28x^4\div56x$

(ii) $-36y^3\div9y^2$

(iii) $66pq^2r^3\div11qr^2$

(iv) $34x^3y^3z^3\div51xy^2z^3$

(v) $12a^8b^8\div\left(-6a^6b^4\right)$

Divide the given polynomial by the given monomial:

$(i)\left(5 x^{2}-6 x\right) \div 3 x$

$(i i)\left(3 y^{8}-4 y^{6}+5 y^{4}\right) \div y^{4}$

$\text { (iii) } 8\left(x^{3} y^{2} z^{2}+x^{2} y^{3} z^{2}+x^{2} y^{2} z^{3}\right) \div 4 x^{2} y^{2} z^{2}$

$(\text { iv })\left(x^{3}+2 x^{2}+3 x\right) \div 2 x$

$(v)\left(p^{3} q^{6}-p^{6} q^{3}\right) \div p^{3} q^{3}$

Q2) Divide the given polynomial by the given monomial.

(i) $\left(5x^2-6x\right)\div3x$

(ii) $3y^8-4y^6+5y^4\div y^4$

(iii) $8\left(x^3y^2z^2+x^2y^3z^2+x^2y^2z^3\right)\ \div\ 4y^2x^2z^2$

(iv) $\left(x^3+2x^2+3x\right)\div\ 2x$

(v) $\left(p^3q^6-p^6q^3\right)\div\ p^3q^3$

Q3)Work out the following divisions.

(i) (10x – 25) ÷ 5

(ii) (10x – 25) ÷ (2x – 5)

(iii) 10y(6y + 21) ÷ 5(2y + 7)

(iv) $9x^2y^2\left(3z-24\right)\div\ 27xy\left(z-8\right)$

(v) 96abc(3a – 12) (5b – 30) ÷ 144(a – 4) (b – 6)

Work out the following divisions:

$\text { (i) }(10 x-25) \div 5$

$\text { (ii) }(10 x-25) \div(2 x-5)$

$\text { (iii) } 10 y(6 y+21) \div 5(2 y+7)$

$\text { (iv) } 9 x^{2} y^{2}(3 z-24) \div 27 x y(z-8)$

$\text { (v) } 96 a b c(3 a-12)(5 b-30) \div 144(a-4)(b-6)$

Q4) Divide as directed.

(i) 5(2x + 1) (3x + 5) ÷ (2x + 1)

(ii) 26xy(x + 5)(y – 4) ÷ 13x(y – 4)

(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)

(iv) $20\left(y+4\right)\left(y^2+5y+3\right)\div5\left(y+4\right)$

(v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

Divide as directed:

(i) 5(2x + 1) (3x + 5) ÷ (2x + 1)

(ii) 26xy(x + 5)(y – 4) ÷ 13x(y – 4)

(iii) 52pqr (p + q) (q + r) (r + p) ÷ 104pq(q + r) (r + p)

(iv) 20(y + 4) (y2 + 5y + 3) ÷ 5(y + 4)

(v) x(x + 1) (x + 2) (x + 3) ÷ x(x + 1)

Factorize the expressions and divide them as directed:

$12 x y\left(9 x^{2}-16 y^{2}\right) \div 4 x y(3 x+4 y)$

Q5)Factorise the expressions and divide them as directed.

(i) $y^2+7y+10\ \div\ \left(y+5\right)$

(ii) $\left(m^2-14m-32\right)\div\ m+2$

(iii) $5p^2-25p+20\ \div\ p-1$

(iv) $4yz\left(z^2+6z-16\right)\div\ 2y\left(z+8\right)$

(v) $5pq\left(p^2-q^2\right)\div2p\left(p+q\right)$

(vi) $12xy\ \left(9x^2-16y^2\right)\div4xy\left(3x+4y\right)$

(vii) $39y^3\left(50y^2-98\right)\div\ 26y^2\left(5y+7\right)$

Factorize the expressions and divide them as directed:

$\left(5 p^{2}-25 p+20\right) \div(p-1)$

Factorize the expressions and divide them as directed:

$4 y z\left(z^{2}+6 z-16\right) \div 2 y(z+8)$

Factorize the expressions and divide them as directed:

$5 p q\left(p^{2}-q^{2}\right) \div 2 p(p+q)$

Factorize the expressions and divide them as directed:

$\left(m^{2}-14 m-32\right) \div(m+2)$

Factorize the expressions and divide them as directed:

$\left(y^{2}+7 y+10\right) \div(y+5)$

Factorize the expressions and divide them as directed:

$39 y^{3}\left(50 y^{2}-98\right) \div 26 y^{2}(5 y+7)$

Questions in Exercise 14.4

Q1) Find and correct the errors in the following mathematical statements.

a) 4(x-5)=4x-5

b) $x\left(3x+2\right)=3x^2+2$

c) $2x+3y=5xy$

d) $x+2x+3x=5x$

e) $5y+2y+y-7y=0$

f) $3x+2x=5x^2$

g) $\left(2x\right)^2+4\left(2x\right)+7=2x^2=8x+7$

h) $\left(2x\right)^2+5x=4x+5x=9x$

i) $\left(3x+2\right)^2+3x^2+6x+4$