Answer
$16x^4+32x^3y+24x^2y^2+8xy^3+y^4$
Work Step by Step
Step 1. Using Pascal's Triangle, we can identify the coefficients of the expansion as $1,4,6,4,1$
Step 2. Combine the know coefficients with corresponding terms $(2x)^ry^{4-r}$ to get:
$(2x+y)^4=(2x)^4+4(2x)^3y+6(2x)^2y^2+4(2x)y^3+y^4=16x^4+32x^3y+24x^2y^2+8xy^3+y^4$
