Answer
$(p-q)^2(p+q)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence:
$p^3-pq^2-p^2q+q^3=\\=p(p^2-q^2)-q(p^2-q^2)\\=(p-q)(p^2-q^2)\\=(p-q)(p+q)(p-q)\\=(p-q)^2(p+q)$
