SChand CLASS 9 Chapter 4 Factorisation Exercise 4(D)

  Exercise 4(D)

Question 1

x² – 4

Sol :

$\begin{aligned} =& x^{2}-4 \\=&\left(x^{2}\right)^{2}-(2)^{2} \\=&(x+2)(x-2) \end{aligned}$

Question 2

y² – 25

Sol :

$\begin{aligned} =& y^{2}-25 \\=&(y)^{2}-(5)^{2} \\=&(y+5)(y-5) \end{aligned}$

Question 3

a² -1

Sol :

$\begin{aligned} =& a^{2}-1 \\=& a^{2}-1^{2} \\=&(a+1)(a-1) \end{aligned}$

Question 4

9z² – 64

Sol :

$=9 z^{2}-64$

$=(3 z)^{2}-(8)^{2}$

$=(3 z+8)(3 z-8)$

Question 5

9x² – b²

Sol :

$=9 x^{2}-b^{2}$

$=(3 x)^{2}-(b)^{2}$

$=(3 x+b)(3 x-b)$

Question 6

25 – x²y²

Sol :

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

$=(5)^{2}-(x y)^{2}$

$=(5-x y)(5+x y)$

Question 7

81a²x² – 49b²y²

Sol :

$=81 a^{2} x^{2}-49 b^{2} y^{2}$

$=(9 a x)^{2}-(7 b y)^{2}$

$=(9 a x+7 b y)(9 a x-7 b y)$

Question 8

$x^2-\frac{1}{4}$

Sol :

$\begin{aligned} =& x^{2}-1 / 4 \\=& x^{2}-\left(\frac{1}{2}\right)^{2} \\=&(x-1 / 2)(x+1 / 2) \end{aligned}$

Question 9

$-25+\frac{1}{64 b^{2}}$

Sol :

$=-25+\frac{1}{64 b^{2}}$

$=\frac{1}{64 b^{2}}-25$

$=\left(\frac{1}{8} b\right)^{2}-(5^{2})$

$=\left(\frac{1}{8} b+5\right)\left(\frac{1}{8} b-5\right)$

Question 10

$\frac{a^{2}}{9}-\frac{b^{2}}{16}$

Sol :

$=\frac{a^{2}}{9}-\frac{b^{2}}{16}$

$=\left(\frac{a}{3}\right)^{2}-\left(\frac{b}{4}\right)^{2}$

$=\left(\frac{a}{3}-\frac{b}{4}\right)\left(\frac{a}{3}+\frac{b}{4}\right)$

Question 11

2.25a² – b²

Sol :

$\begin{aligned} & =2 \cdot 25 a^{2}-b^{2} \\ &=(1\cdot 5 a)^{2}-(b)^{2} \\&=(1 \cdot 5 a+b)(1.5 a-b) \end{aligned}$

Question 12

$36a^8 – 121$

Sol :

$=36 a^{8}-121$

$=\left(6 a^{4}\right)^{2}-(11)^{2}$

$=\left(6 a^{4}-11\right)\left(6 a^{4}+11\right)$

Question 13

54² – 36²

Sol :

$=54^{2}-36^{2}$

$=(54+36)(54-36)$

=90×18=1620

Question 14

(3.2)² – (1.8)²

Sol :

$\begin{aligned} =&(3\cdot 2)^{2}-(1.8)^{2} \\=&(3.2+1.8)(3.2-1.8) \\=& 5.0 \times 1.4 \\=& 7.0 \Rightarrow 7 \end{aligned}$