Question

Using Binomial Theorem, evaluate \((96)^3\).

Answer 1

Given:

96³

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Step 1: Rewrite using Binomial Theorem

96 = 100 − 4

∴ 96³ = (100 − 4)³

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Step 2: Apply Binomial Theorem

(a − b)³ = a³ − 3a²b + 3ab² − b³

Let a = 100 and b = 4

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Step 3: Substitute values

(100 − 4)³ =

100³ − 3·100²·4 + 3·100·4² − 4³

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Step 4: Simplify

100³ = 1,000,000
3·100²·4 = 120,000
3·100·16 = 4,800
4³ = 64

96³ =

1,000,000 − 120,000 + 4,800 − 64

= 884,736

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Final Answer:

96³ = 884,736