13. Suppose $x-y=1$. Find the value of
$$
x^{4}-x y^{3}-x^{3} y-3 x^{2} y+3 x y^{2}+y^{4}
$$
13 Ans: 1.
The expression $=(x-y)\left[(x-y)\left(x^{2}+x y+y^{2}\right)-3 x y\right]$. Substituting $x-y=1$, one sees that the expression $=(x-y)^{2}=1$.