Special Products 5

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

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

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

= \(125{x}^{9}-3\left(25{x}^{6}\right)\left(3{y}^{2}\right)+3\left(5{x}^{3}\right)\left(9{y}^{4}\right)-27{y}^{6}\)

= \(125{x}^{9}-225{x}^{6}{y}^{2}+135{x}^{3}{y}^{4}-27{y}^{6}\)