#### Answer

$p^4 + 8 p^3 q + 24 p^2 q^2 + 32 p q^3 + 16 q^4$

#### Work Step by Step

$(x+y)^n=\binom{n}{0}x^ny^0+\binom{n}{1}x^{n-1}y^1+...+\binom{n}{a}x^{n-a}y^a+..\binom{n}{n}x^{0}y^n$
Here: $n=4$, $x=p$, $y=2q$
$(p+2q)^4=\binom{4}{0}p^4(2q)^0+\binom{4}{1}p^{4-1}(2q)^1+\binom{4}{2}p^{4-2}(2q)^2+\binom{4}{3}p^{4-3}(2q)^3+\binom{4}{4}p^{4-4}(2q)^4=$
$p^4 + 8 p^3 q + 24 p^2 q^2 + 32 p q^3 + 16 q^4$