22. Five mark exercise problems IV

If \(S_n\) \(=\) \((x + y) + (x^2 + xy + y^2) + (x^3 + x^2y + xy^2 + y^3) +...+\) \(n\) \(\text{terms}\) then prove that \((x - y)S_n\) \(=\) \(\bigg[\)\(\frac{x^2(x^n - 1)}{x - 1}\) \(-\) \(\frac{y^2(y^n - 1)}{y - 1}\)\(\bigg]\)