Random Special Products

= \({\left(A+B\right)}^3\) , where \(A={x}^{4}\) and \(B=2{y}^{5}\)

= \(A^3+3A^2B+3AB^2+B^3\)

= \({\left({x}^{4}\right)}^{3}+3{\left({x}^{4}\right)}^{2}\left(2{y}^{5}\right)+3\left({x}^{4}\right){\left(2{y}^{5}\right)}^{2}+{\left(2{y}^{5}\right)}^{3}\)

= \({x}^{12}+3\left({x}^{8}\right)\left(2{y}^{5}\right)+3\left({x}^{4}\right)\left(4{y}^{10}\right)+8{y}^{15}\)

= \({x}^{12}+6{x}^{8}{y}^{5}+12{x}^{4}{y}^{10}+8{y}^{15}\)