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Question
Factorize x (x3 - y3 ) + 3xy ( x - y )
Solution
Elaborating x3 - y3 using identity a3 - b3 = (a - b)(a2 + ab + b2 )
= x ( x - y)(x2 + xy + y2 ) + 3xy (x - y )
Taking common x( x - y ) in both the terms
= x ( x - y){x2 + xy + y2 + 3y}
∴ x (x3 - y3 ) + 3xy ( x - y) = x ( x - y )(x2 + xy + y2 + 3y)
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