Special Products 5

\(\, \, \, \,{\left(4{x}^{5}-11{y}^{3}\right)}^{3}\)

= \({\left(A-B\right)}^3\) , where \(A=4{x}^{5}\) and \(B=11{y}^{3}\)

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

= \({\left(4{x}^{5}\right)}^{3}-3{\left(4{x}^{5}\right)}^{2}\left(11{y}^{3}\right)+3\left(4{x}^{5}\right){\left(11{y}^{3}\right)}^{2}-{\left(11{y}^{3}\right)}^{3}\)

= \(64{x}^{15}-3\left(16{x}^{10}\right)\left(11{y}^{3}\right)+3\left(4{x}^{5}\right)\left(121{y}^{6}\right)-1331{y}^{9}\)

= \(64{x}^{15}-528{x}^{10}{y}^{3}+1452{x}^{5}{y}^{6}-1331{y}^{9}\)

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