Special Products 5

= \({\left(A-B\right)}^3\) , where \(A=9{x}^{2}\) and \(B=8{y}^{3}\)

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

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

= \(729{x}^{6}-3\left(81{x}^{4}\right)\left(8{y}^{3}\right)+3\left(9{x}^{2}\right)\left(64{y}^{6}\right)-512{y}^{9}\)

= \(729{x}^{6}-1944{x}^{4}{y}^{3}+1728{x}^{2}{y}^{6}-512{y}^{9}\)