In two or more complete sentences, prove how to find the third term of the expansion of (2x + y)4.

Answer:The third term is [tex]24x^2y^2[/tex]Step-by-step explanation:The formula used to find the third term of the expansion (2x+y)^4 is called Binomial TheoremThe Binomial Theorem is:[tex](x+a)^n = \sum_{k=0}^{n} {n \choose k}x^ka^{n-k}\\[/tex]In the given question x = 2xa = yn = 4We have to find the third term, so value of k will be 2 as k starts from 0Putting the values in the Binomial Theorem[tex]= {4 \choose 2}(2x)^2(y)^{4-2}\\= {4 \choose 2}4x^2(y)^{2}[/tex][tex]{n \choose k}==\frac{n!}{k!(n-k)!}[/tex]Putting the values: [tex]= {4 \choose 2}4x^2(y)^{2}\\=\frac{4!}{2!(4-2)!}4x^2(y)^{2}\\=\frac{4!}{2!2!}4x^2y^{2}\\=\frac{4*3*2*1}{2*2}4x^2y^{2}\\=\frac{24}{4}4x^2y^{2}\\=6*4x^2y^{2}\\=24x^2y^2[/tex]So, the third term is [tex]24x^2y^2[/tex]