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Question
Factorize 8x3 + 27 y3 + 36x2 y + 54xy2
Solution
8x3 + 27 y3 + 36x2 y + 54xy2
= (2x)3 + (3y)3 + 3 × (2x)2 × 3y + 3 × (2x)(3y )2
= (2x + 3y )3 [∵ a3 + b3 + 3a2b + 3ab2 = (a + b)3]
= (2x + 3y )(2x + 3y )(2x + 3y )
∴ 8x3 + 27 y3 + 36x2 y + 54xy2 = (2x + 3y )(2x + 3y )(2x + 3y )
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