Answer
$x^5+10x^4y+40x^3y^2+80x^2y^3+80xy^4+32y^5$
Work Step by Step
Apply Binomial Theorem.
$(a+b)^n=\sum_{r=0}^n\dbinom{n}{r}(a)^{n-r}b^r$
$(x+2y)^5=\dbinom{5}{0}(x)^5(2y)^0+\dbinom{5}{1}(x)^4(2y)^1+\dbinom{5}{1}(x)^3(2y)^2+\dbinom{5}{3}(x)^2(2y)^3+\dbinom{5}{4}(x)^1(2y)^4+\dbinom{5}{5}(x)^0(2y)^5$
or, $=x^5+(5)(x^4)(2y)+10x^3(4y^2)+10x^2(8y^3)+80xy^4+32y^5$
or, $=x^5+10x^4y+40x^3y^2+80x^2y^3+80xy^4+32y^5$
