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Question
Factorise the following:
9(a - b)2 - (a + b)2
Sum
Solution
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).
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Method of Factorisation : Difference of Two Squares
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