Question

Prove this polynomial identity

Answer 1

Answer:

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