Random Special Products

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

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

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

= \(8{x}^{15}+3\left(4{x}^{10}\right)\left(5{y}^{5}\right)+3\left(2{x}^{5}\right)\left(25{y}^{10}\right)+125{y}^{15}\)

= \(8{x}^{15}+60{x}^{10}{y}^{5}+150{x}^{5}{y}^{10}+125{y}^{15}\)