Using the Binomial Theorem,evaluate (96)^{3}. | vedclass

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(A) We can express $96$ as the difference of two numbers whose powers are easier to calculate,and then apply the Binomial Theorem.It can be written th

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$884736$

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(A) We can express $96$ as the difference of two numbers whose powers are easier to calculate,and then apply the Binomial Theorem.It can be written that $96 = 100 - 4$.Therefore,$(96)^{3} = (100 - 4)^{3}$.Using the Binomial Theorem formula $(a - b)^{n} = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} (-b)^{k}$:$(100 - 4)^{3} = \binom{3}{0}(100)^{3} - \binom{3}{1}(100)^{2}(4) + \binom{3}{2}(100)(4)^{2} - \binom{3}{3}(4)^{3}$$= (1)(1000000) - 3(10000)(4) + 3(100)(16) - (1)(64)$$= 1000000 - 120000 + 4800 - 64$$= 880000 + 4800 - 64$$= 884800 - 64$$= 884736$

Using the Binomial Theorem,evaluate $(96)^{3}$.

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