Question

$pq 2 + 4pq + 4p$
​

Answer 1

$pq^2+4pq+4p=p\cdot(q^2+4q+4)=p\cdot(q+2)^2$

Observe:

$(a+b)^2=a^2+2ab+b^2\\ \\(q+2)^2=q^2+2\cdot q\cdot2+2^2\\ \\(q+2)^2=q^2+4q+4$