Using binomial theorem, evaluate each of the following:
$(96)^{3}$

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Solution

$\begin{matrix} {(\begin{matrix} 96 \end{matrix})}^{3} {(96)}^{3} = {(100 - 4)}^{3} =^{3} C_{0} {(100)}^{3} +^{3} C_{1} {(100)}^{2} - {(- 4)}^{1} +^{3} C_{2} (100) {(- 4)}^{2} +^{3} C_{3} {(100)}^{0} {(- 4)}^{3} = 1000000 - 120000 + 4800 - 64 = 1004800 - 120064 = 884736. \end{matrix}$

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