Answer
$32x^5+80x^4y^2+80x^3y^4+40x^2y^6+10xy^8+y^{10} $
Work Step by Step
Step 1. Use the Binomial Theorem or the Pascal's Triangle, we can obtain the coefficients as $1,5,10,10,5,1$
Step 2. Combine the coefficients with the corresponding power terms $(2x)^{5-r+1}(y^2)^{r-1}, r=1,2,3,4,5$, we can write the expansion as:
$(2x+y^2)^5=(2x)^5+5(2x)^4(y^2)+10(2x)^3(y^2)^2+10(2x)^2(y^2)^3+5(2x)(y^2)^4+(y^2)^5
=32x^5+80x^4y^2+80x^3y^4+40x^2y^6+10xy^8+y^{10} $
