Special Products 5

= \({\left(A-B\right)}^3\) , where \(A=5{x}^{2}\) and \(B={y}^{4}\)

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

= \({\left(5{x}^{2}\right)}^{3}-3{\left(5{x}^{2}\right)}^{2}\left({y}^{4}\right)+3\left(5{x}^{2}\right){\left({y}^{4}\right)}^{2}-{\left({y}^{4}\right)}^{3}\)

= \(125{x}^{6}-3\left(25{x}^{4}\right)\left({y}^{4}\right)+3\left(5{x}^{2}\right)\left({y}^{8}\right)-{y}^{12}\)

= \(125{x}^{6}-75{x}^{4}{y}^{4}+15{x}^{2}{y}^{8}-{y}^{12}\)