Answer
$r^{10} + 5 r^8 s + 10 r^6 s^2 + 10 r^4 s^3 + 5 r^2 s^4 + s^5$
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: $n=7$,
$(r^2+s)^5=\binom{5}{0}(r^2)^7s^0+\binom{5}{1}(r^2)^{5-1}s^1+\binom{5}{2}(r^2)^{5-2}s^2+\binom{5}{3}(r^2)^{5-3}s^3+\binom{5}{4}(r^2)^{5-4}s^4+\binom{5}{5}(r^2)^{5-5}s^5=$
$r^{10} + 5 r^8 s + 10 r^6 s^2 + 10 r^4 s^3 + 5 r^2 s^4 + s^5$
