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Question
Factorize 125x3 - 27 y3 - 225x2 y +135xy2
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Solution
125x3 - 27 y3 - 225x2 y +135xy2
= (5x)3 - (3y )3 - 3 × (5x)2 ´ 3y + 3 × (5x)(3y )2
= (5x - 3y )3 [∵ a3 - b3 - 3a2b + 3ab2 = (a - b)3]
= (5x - 3y )(5x - 3y )(5x - 3y )
∴ 125x3 - 27 y3 - 225x2 y +135xy2 = (5x - 3y)(5x - 3y )(5x - 3y )
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