Question

Expand the following binomial:
${(2x-y)}^5$

Answer 1

Using Binomial expansion,

$(2x-y{)}^5={}^5{C}_0(2x{)}^5+{}^5{C}_1\left(2x{)}^4\right(-y)+{}^5{C}_2(2x{)}^3(-y{)}^2+{}^5{C}_3(2x{)}^2(-y{)}^3+{}^5{C}_2(2x\left)\right(-y{)}^4+{}^5{C}_1(-y{)}^5$

On solving and substituting values we get

$(2x-y{)}^5=32x^5-80x^{4}y+80x^3{y}^2-40x^2{y}^3+10x{y}^4-y^5$