Answer
$(x+2y)^{4}=x^{4}+8x^{3}y+24x^{2}y^{2}+32xy^{3}+16y^{4}$
Work Step by Step
We expand using the Binomial Theorem:
$(x+2y)^{4}=\left(\begin{array}{l} 4\\ 0 \end{array}\right)x^{4}+\left(\begin{array}{l} 4\\ 1 \end{array}\right)x^{3}\cdot 2y^1+\left(\begin{array}{l} 4\\ 2 \end{array}\right)x^{2}\cdot 4y^{2}+\left(\begin{array}{l} 4\\ 3 \end{array}\right)x^{1}8y^{3}+\left(\begin{array}{l} 4\\ 4 \end{array}\right)16y^{4}=1*x^{4}+4*2x^{3}y+6*4x^{2}y^{2}+4*8xy^{3}+1*16y^{4}=x^{4}+8x^{3}y+24x^{2}y^{2}+32xy^{3}+16y^{4}$
