Question

prove that

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

Answer 1

(x+y)^3

=(x+y)(x+y)(x+y)

=(x^2 + y^2 + 2xy)(x+y)

=(x^3 + y^3 + xy^2 + yx^2 + 2xy^2 +2yx^2)

=x^3 + y^3 +3xy^2 + 3yx^2

=x^3 + y^3 + 3xy(x+y)