Answer
$p^5 - 5 p^4 q + 10 p^3 q^2 - 10 p^2 q^3 + 5 p q^4 - q^5$
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: $n=5$,
$(p-q)^5=\binom{5}{0}p^5(-q)^0+\binom{5}{1}p^{5-1}(-q)^1+\binom{5}{2}p^{5-2}(-q)^2+\binom{5}{3}p^{5-3}(-q)^3+\binom{5}{4}p^{5-4}(-q)^1+\binom{5}{5}p^{5-5}(-q)^5=$
$p^5 - 5 p^4 q + 10 p^3 q^2 - 10 p^2 q^3 + 5 p q^4 - q^5$
