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Factorize x (x^{3} - y^{3} ) + 3xy ( x - y )

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#### Solution

Elaborating x^{3} - y^{3} using identity a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2} )

= x ( x - y)(x^{2} + xy + y^{2} ) + 3xy (x - y )

Taking common x( x - y ) in both the terms

= x ( x - y){x^{2} + xy + y^{2} + 3y}

∴ x (x^{3} - y^{3} ) + 3xy ( x - y) = x ( x - y )(x^{2} + xy + y^{2} + 3y)

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