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]$