Answer
$x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$
Work Step by Step
We are given the expression:
$(x^2+y^2)^5$
Use the Binomial Theorem to expand the expression:
$(x^2+y^2)^5=\sum_{k=0}^5 \binom{5}{k}(x^2)^{5-k}(y^2)^k$
$=\binom{5}{0}(x^2)^5(y^2)^0+\binom{5}{1}(x^2)^4(y^2)^1+\binom{5}{2}(x^2)^3(y^2)^2+\binom{5}{3}(x^2)^2(y^2)^3+\binom{5}{4}(x^2)^1(y^2)^4+\binom{5}{5}(x^2)^0(y^2)^5$
$=x^{10}+5x^8y^2+10x^6y^4+10x^4y^6+5x^2y^8+y^{10}$