Special Products 5

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

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

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

= \(27{x}^{3}-3\left(9{x}^{2}\right)\left(2{y}^{2}\right)+3\left(3x\right)\left(4{y}^{4}\right)-8{y}^{6}\)

= \(27{x}^{3}-54{x}^{2}{y}^{2}+36x{y}^{4}-8{y}^{6}\)