ML AGGARWAL CLASS 8 CHAPTER 11 Factorisation Exercise 11.2

 Exercise 11.2

Solution 1

Sol :

(i)

$\begin{aligned} & x^{2}+x y-x-y \\ \Rightarrow & x(x+y)-1(x+y) \\ \Rightarrow &(x+y)(x-1) \end{aligned}$

(ii)

$\begin{aligned} & y^{2}-y z-5 y+5 z \\ \Rightarrow & y(y-z)-5(y-z) \\ \Rightarrow &(y-z)(y-5) \end{aligned}$

Solution 2

Sol :

(i) 

$\begin{aligned} & 5 x y+7 y-5 y^{2}-7 x \\ \Rightarrow & 5 x y-5 y^{2}+7 y-7 x . \\ \Rightarrow & 5 x y-5 y^{2}-7 x+7 y \\ \Rightarrow & 5 y(x-y)-7(x-y) \\ \rightarrow &(x-y)(5 y-7) \end{aligned}$

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

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

5p(p-2)-8q(p-2)

(p-2)(5p-8q)

Solution 3

Sol :

(i) 

$\begin{aligned} & a^{2} b-a b^{2}+3 a-3 b \\ \Rightarrow & a b(a-b)+3(a-b) \\ \Rightarrow &(a-b)(a b+3) \end{aligned}$

(ii)

$\begin{aligned} & x^{3}-3 x^{2}+x-3 \\=& x^{2}(x-3)+1(x-3) \\ \Rightarrow &(x-3)\left(x^{2}+1\right) \end{aligned}$

Solution 4

Sol :

(i) 

$\begin{aligned} & 6 x y^{2}-3 x y-10 y+5 \\ \Rightarrow & 3 x y(2 y-1)-5(2 y-1) \\ \Rightarrow &(2 y-1)(3 x y-5) \end{aligned}$

(ii) 3ax-6ay-8by+4 bx

3a(x-2 y)+2b(-2y+x)

$\Rightarrow 3 a(x-2 y)+2 b(x-2 y)$

$\Rightarrow \quad(x-2 y)(3 a+2 b)$

Solution 5

Sol :

(i) $x^{2}+x y(1+y)+y^{3}$\

$\Rightarrow x^{2}+x y+x y^{2}+y^{3}$

$\Rightarrow \quad x(x+y)+y^{2}(x+y)$

$\Rightarrow \quad(x+y)\left(x+y^{2}\right)$

(ii) $y^{2}-x y(1-x)-x^{3}$

$\Rightarrow y^{2}-x y+x^{2} y-x^{3}$

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

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

Solution 6

Sol :

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

$a b^{2}+a b-b-1$

ab(b+1)-(b+1)

(b+1)(a b-1)

(ii) 2a-4b-xa+2bx

=2(a-2b)-x(a-2b)

=(a-2b)(2-x)

Solution 7

Sol :

(i) 5ph-10qk+2rph-4q rk

=5(p h-2 q k)+2 r(p h-2 q k)

$=\left(p h-2 qk\right)(5+2 r)$

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

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

=x(x-a)-2 b(x-a)

=(x-a)(x-2 b)

Solution 8

Sol :

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

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

=a x(b x-a y)+b y(a y-b x)

=a x(b x-a y)-b y(b x-a y)

=(b x-a y)(a x-b y)

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

=$a^{2} x^{2}+b^{2} y^{2}+2 a x \cdot b y+b^{2} x^{2}+a^{2} y^{2}-2 b x .a y$

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

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

Solution 9

 Sol :

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

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

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

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

 

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

=3xy(x-1)+12(x-1)

=(x-1)(3 x y+12)

=(x-1)3(x y+4)

=$\therefore \quad 3(x-1)(x y+4)$

Solution 10

Sol :

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

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

=a b(a+b)-b c(a+b)+x y(a+b)

=(a+b)(a b-b c+x y)

 

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

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

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

Solution 11

Sol :

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

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

=$(x-1) \quad(1-(x-1)+a)$

=(x-1)(1-x+1+a)

=(x-1)(2-x+a)

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

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

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

=(a+b y)(1+a-a x-b y)