Question

derive an identity for (x+y)^3

Answer 1

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