Answer
$(x^{10}+2y^{5})^{2}$
Work Step by Step
Given the polynomial
$(x^{10})^{2}$ + $4x^{10}y^{5}$ + $(2y^{5})^{2}$
We see that the polynomial has the first and last term squared and the middle term is +2 times the first and last term. Thus it follows the rule of
$a^{2}$ + 2ab + $b^{2}$ = $(a+b)^{2}$
In this polynomial a= $x^{10}$ and b=$2y^{5}$
$x^{10}$ + 2($x^{10})(2y^{5}$) + $2y^{5}$ = $(x^{10}+2y^{5})^{2}$
