Special Products 4

\(\, \, \, \,{\left(11{x}^{6}+2{y}^{6}\right)}^{3}\)

= \({\left(A+B\right)}^3\) , where \(A=11{x}^{6}\) and \(B=2{y}^{6}\)

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

= \({\left(11{x}^{6}\right)}^{3}+3{\left(11{x}^{6}\right)}^{2}\left(2{y}^{6}\right)+3\left(11{x}^{6}\right){\left(2{y}^{6}\right)}^{2}+{\left(2{y}^{6}\right)}^{3}\)

= \(1331{x}^{18}+3\left(121{x}^{12}\right)\left(2{y}^{6}\right)+3\left(11{x}^{6}\right)\left(4{y}^{12}\right)+8{y}^{18}\)

= \(1331{x}^{18}+726{x}^{12}{y}^{6}+132{x}^{6}{y}^{12}+8{y}^{18}\)

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