Question

1. Factorise:
(vi) 64(a - b)2 - 81(a + b)2​

Answer 1

$Given \: 64(a-b)^{2} - 81(a+b)^{2}$

$= [8(a-b)]^{2} - [9(a+b)]^{2}$

$= ( 8a - 8b )^{2} - ( 9a - 9b )^{2}$

/* By algebraic identity */

$\boxed{\pink{ x^{2} - y^{2} = (x+y)(x-y) }}$

$= [ (8a-8b) + ( 9a-9b) ] [ (8a-8b) - ( 9a-9b) ]$

$= (8a-8b + 9a-9b) (8a-8b- 9a+ 9b)$

$=( 17a - 17b)( -a + b )$

$= 17(a-b)(b-a)$

Therefore.,

$\red{ Factors \:of \: 64(a-b)^{2} - 81(a+b)^{2} }$

$\green { = 17(a-b)(b-a) }$

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