Question
Factorise the following:$9(a - b)^2 - (a + b)^2$
✓
Answer
$9(a - b)^2 - (a + b)^2$
$= [3(a - b)]^2 - (a + b)^2$
$= [3(a - b) - (a + b)][3(a - b) + (a + b)]$
$= (3a - 3b - a - b)(3a - 3b + a + b)$
$= (2a - 4b)(4a - 2b)$
$= 2(a - 2b)2(2a - b)$
$= 4(a - 2b)(2a - b).$
$= [3(a - b)]^2 - (a + b)^2$
$= [3(a - b) - (a + b)][3(a - b) + (a + b)]$
$= (3a - 3b - a - b)(3a - 3b + a + b)$
$= (2a - 4b)(4a - 2b)$
$= 2(a - 2b)2(2a - b)$
$= 4(a - 2b)(2a - b).$
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