22. Suppose that $x-y=1$. Find the value of $x^{4}-x y^{3}-x^{3} y-3 x^{2} y+3 x y^{2}+y^{4}$.
22. Ans: 1 .
We manipulate the expression and replace $x-y$ by 1 whenever necessary:
$$
\begin{aligned}
& x^{4}-x y^{3}-x^{3} y-3 x^{2} y+3 x y^{2}+y^{4} \\
= & x^{3}(x-y)-y^{3}(x-y)-3 x y(x-y) \\
= & (x-y)\left(x^{2}+x y+y^{2}\right)-3 x y \\
= & (x-y)^{2} \\
= & 1 .
\end{aligned}
$$