Special Products 4
\(\, \, \, \,{\left(4{x}^{5}+3{y}^{5}\right)}^{3}\)
= \({\left(A+B\right)}^3\) , where \(A=4{x}^{5}\) and \(B=3{y}^{5}\)
= \(A^3+3A^2B+3AB^2+B^3\)
= \({\left(4{x}^{5}\right)}^{3}+3{\left(4{x}^{5}\right)}^{2}\left(3{y}^{5}\right)+3\left(4{x}^{5}\right){\left(3{y}^{5}\right)}^{2}+{\left(3{y}^{5}\right)}^{3}\)
= \(64{x}^{15}+3\left(16{x}^{10}\right)\left(3{y}^{5}\right)+3\left(4{x}^{5}\right)\left(9{y}^{10}\right)+27{y}^{15}\)
= \(64{x}^{15}+144{x}^{10}{y}^{5}+108{x}^{5}{y}^{10}+27{y}^{15}\)
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Differential Calculus
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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)