Question

1. Express the following as in the form of (a+b)(a-b)
(1) asquare - 64
(ii) 20asquare - 45b
(iii) 36x?y? - 8
(iv) xsquare - 2xy + ysquare - 2
(v) 49x² - 1​

Answer 1

AnswEr :

$\large\orange{\boxed{ \star \: \bold{ ( {a}^{2} - {b}^{2}) = (a + b)(a - b) }}}$

$\blacksquare \: \: \bold { {a}^{2} - 64 }$

$\implies \tt{ ({a})^{2} - ( {8})^{2} }$

$\blue{ \implies \tt{(a + 8)(a - 8)}}$

$\rule{100}{2}$

$\blacksquare \: \: \bold{20 {a}^{2} - 45b }$

$\implies \tt{(2 \sqrt{5}a)^{2} - (3 \sqrt{5b})^{2} }$

$\blue{ \implies \tt{(2 \sqrt{5}a + 3 \sqrt{5b})(2 \sqrt{5}a - 3 \sqrt{5b} ) }}$

$\rule{100}{2}$

$\blacksquare \: \: \bold{36 {x}^{2} {y}^{2} - 8 }$

$\implies \tt{( {6xy})^{2} - ({2 \sqrt{2} })^{2} }$

$\blue{ \implies \tt{(6xy + 2 \sqrt{2})(6xy - 2 \sqrt{2} ) }}$

$\rule{100}{2}$

$\blacksquare \: \: \bold{ {x}^{2} - 2xy + {y}^{2} - 2 }$

$\implies \tt{ {(x - y)}^{2} - ({ \sqrt{ 2} })^{2} }$

$\blue{ \implies \tt{(x - y + \sqrt{2})(x - y - \sqrt{2}) }}$

$\rule{100}{2}$

$\blacksquare \: \: \bold{49 {x}^{2} - 1}$

$\implies \tt{ ({7x})^{2} - ({1})^{2} }$

$\blue{ \implies \tt{(7x + 1)(7x - 1)}}$

$\rule{100}{2}$

Answer 2

Answer:

(a+b) (a-b)

a) a²-64

= a2- (8)2

= (a - 8) ( a +8)

b)49x²-1

= (7x)2 - (1)2

= (7x - 1) (7x + 1)