Special Products 5
\(\, \, \, \,{\left(2{x}^{4}-3{y}^{2}\right)}^{3}\)
= \({\left(A-B\right)}^3\) , where \(A=2{x}^{4}\) and \(B=3{y}^{2}\)
= \(A^3-3A^2B+3AB^2-B^3\)
= \({\left(2{x}^{4}\right)}^{3}-3{\left(2{x}^{4}\right)}^{2}\left(3{y}^{2}\right)+3\left(2{x}^{4}\right){\left(3{y}^{2}\right)}^{2}-{\left(3{y}^{2}\right)}^{3}\)
= \(8{x}^{12}-3\left(4{x}^{8}\right)\left(3{y}^{2}\right)+3\left(2{x}^{4}\right)\left(9{y}^{4}\right)-27{y}^{6}\)
= \(8{x}^{12}-36{x}^{8}{y}^{2}+54{x}^{4}{y}^{4}-27{y}^{6}\)
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Analytic Geometry
Differential Calculus
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Copyright © Dayal D. Purohit, Ph.D.(Mathematics)