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Question
Factorize 8a3 – 27b3 – 36a2b + 54ab2
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Solution
8a3 - 27b3 - 36a2b + 54ab2
= (2a)3 - (3b)3 - 3 × (2a)2 3b + 3(2a)(3b)2
= (2a - 3b)3 [∵ a3 - b3 - 3a2b + 3ab2 = (a - b)3 ]
= (2a - 3b)(2a - 3b)(2a - 3b)
∴ 8a3 - 27b3 - 36a2b + 54ab2 = (2a - 3b)(2a - 3b)(2a - 3b)
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