Question
Factorise: $25(a - 5b)^2 - 4(a - 3b)^2$
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Answer
$25(a - 5b)^2 - 4(a - 3b)^2$
$= [5 (a - 5b)]^2 - [2(a - 3b)]^2$
$= (5a - 25b)^2 - (2a - 6b)^2$
$= (5a - 25b + 2a - 6b)(5a - 25b - 2a + 6b)$
$.....[a^2 - b^2 = (a + b)(a - b)]$
$= (7a - 31b)(3a - 19b)$
$= [5 (a - 5b)]^2 - [2(a - 3b)]^2$
$= (5a - 25b)^2 - (2a - 6b)^2$
$= (5a - 25b + 2a - 6b)(5a - 25b - 2a + 6b)$
$.....[a^2 - b^2 = (a + b)(a - b)]$
$= (7a - 31b)(3a - 19b)$
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