SChand CLASS 9 Chapter 4 Factorisation Exercise 4(B)

 Exercise 4(B)

Question 1

bx+2b+cx+2c

Sol :

=bx+2b+cx+2c

=bx+cx+2b+2c

=x(b+c)+2(b+c)

Question 2

y² + 2y² + 3y + 6

Sol :

$=y^{3}+2 y^{2}+3 y+6$

$=y^{2}(y+2)+3(y+2)$

$=(y+2)\left(y^{2}+3\right)$

Question 3

xa + 3b + xb + 3a

Sol :

$\begin{aligned} & x a+3 b+x b+3 a \\=& x a+x b+3 a+3 b \\=& x(a+b)+3(a+b) \\=&(x+3)(a+b) \end{aligned}$

Question 4

8xy + 5zy – 8xt – 5zt

Sol :

=8xy+5zy-8xt-5zt

=8xy-8xt+5zy-5zt

=8x(y-t)+5(y-t)

=(8x+5z)(y-t)

Question 5

8kl + 12ml – 12mn – 8kn

Sol :

=8kl+12ml-12mn-8kn

=8kl-8kn+12ml-12mn

=8k(l-n)+12m(l-n)

=(8k+12m)(l-n)

Question 6

32 (x + y)² – 2x – 2y

Sol :

$=32(x+y)^{2}-2x-2y$

=32(x+y)(x+y)-2(x-y)

=2(x-y)(16(x+y)-1)

=2(x+y)(16 x+16 y-1)

Question 7

x³ – x² + ax + x – a – 1

Sol :

$=x^{3}-x^{2}+a x+x-a-1$

$=x^{3}-x^{2}+a x-a+x-1$

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

$=(x-1)\left(x^{2}+a+1\right)$

Question 8

ab (c² + 1) + c (a² + b²)

Sol :

$=a b\left(c^{2}+1\right)+c\left(a^{2}+b^{2}\right)$

$=a b c^{2}+a b+a^{2} c+b^{2} c$

$=a b c^{2}+a^{2} c+b^{2} c+a b$

=ac(bc+a)+b(bc+a)

=(bc+a)(ac+b)

Question 9

a³ – a² + xa + a – x – 1

Sol :

$=a^{3}-a^{2}+x a+a-x-1$

$=a^{3}-a^{2}+x a-x+a-1$

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

$=(a-1)\left(a^{2}+x+1\right)$

Question 10

6a³b + 3a²b² – 2a²b – ab²

Sol :

$=6 a^{3} b+3 a^{2} b^{2}-2 a^{2} b-a b^{2}$

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

$=(2 a+b)\left(3 a^{2} b-2 b\right)$

=(2a+b)ab(3a-1)

=ab(3a-1)(2a+b)

Question 11

a³ + ab (1 – 2a) – 2b²

Sol :

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

$=a^{3}+a b-2 a^{2} b-2 b^{2}$

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

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

Question 12

(p² + 1)q – p² – q²

Sol :

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

$=p^{2} q+2-p^{2}-q^{2}$

$=p^{2} r-p^{2}-q^{2}+q$

$=p^{2}(q-1)-q(q-1)$

$=(q-1)\left(p^{2}-q\right)$