等式の証明

問題次の等式を証明せよ。$${\small (1)}~ (x+y)(x^2+y^2)$$$$~~~~~=x^3+y^3+xy(x+y)$$$${\small (2)}~ a^5-b^5$$$$~~~~~=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)$$