Special Products 5

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

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

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

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

= \({x}^{9}-3{x}^{6}{y}^{3}+3{x}^{3}{y}^{6}-{y}^{9}\)