Answer
$16x^4+40x^2y+25y^2$
Work Step by Step
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $(4x^2+5y)^2=(4x^2)^2+2\cdot4x^2\cdot5y+(5y)^2=16x^4+40x^2y+25y^2$