Special Products 5

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

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

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

= \({x}^{6}-3\left({x}^{4}\right)\left(2{y}^{3}\right)+3\left({x}^{2}\right)\left(4{y}^{6}\right)-8{y}^{9}\)

= \({x}^{6}-6{x}^{4}{y}^{3}+12{x}^{2}{y}^{6}-8{y}^{9}\)