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Question
Factorize the following expressions:
54x6y + 2x3y4
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Solution
54x6 y + 2x3 y4
= 2x3 y (27x3 + y3)
= 2x3 y ((3x)3 + y3)
= 2x3 y (3x + y)((3x)2 - 3 x xy + y2) [ ∵ a3 + b3 = (a + b)(a2 - ab + b2)]
= 2x3 y (3x + y)(9x2 - 3xy + y2)
∴ 54x6 y + 2x3 y4 = 2x3 y (3x + y )(9x2 - 3xy + y2)
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