Question

Prove this polynomial identity

Answer 1

`(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) )`