Remember the following formula for a squared binomial:
[tex](a+b)^2=a^2+2ab+b^2[/tex]Then, for the given binomial:
[tex](x^2+10y^2)^2[/tex]Use:
[tex]\begin{gathered} a=x^2 \\ b=10y^2 \end{gathered}[/tex]Then:
[tex]\begin{gathered} (x^2+10y^2)^2=(x^2)^2+2(x^2)(10y^2)+(10y^2)^2 \\ =x^4+20x^2y^2+100y^4 \end{gathered}[/tex]Therefore:
[tex](x^2+10y^2)^2=x^4+20x^2y^2+100y^4[/tex]