Special Products 5

= \({\left(A-B\right)}^3\) , where \(A=7{x}^{3}\) and \(B=8{y}^{3}\)

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

= \({\left(7{x}^{3}\right)}^{3}-3{\left(7{x}^{3}\right)}^{2}\left(8{y}^{3}\right)+3\left(7{x}^{3}\right){\left(8{y}^{3}\right)}^{2}-{\left(8{y}^{3}\right)}^{3}\)

= \(343{x}^{9}-3\left(49{x}^{6}\right)\left(8{y}^{3}\right)+3\left(7{x}^{3}\right)\left(64{y}^{6}\right)-512{y}^{9}\)

= \(343{x}^{9}-1176{x}^{6}{y}^{3}+1344{x}^{3}{y}^{6}-512{y}^{9}\)