Question

Factorize x (x³ - y³ ) + 3xy ( x - y )

Answer 1

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)