Question:
Using Binomial Theorem, evaluate \((96)^3\).
Using Binomial Theorem, evaluate \((96)^3\).
Updated On: Oct 25, 2023
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Solution and Explanation
\(96 \) can be expressed as the sum or difference of two numbers whose powers are easier to calculate and then, binomial theorem can be applied.
It can be written that, \(96 = 100 - 4\)
∴ \((96)^3=(100-4)^3\)
=\(^3C_0(100)^3 - ^3C_1(100)^2(4)+ ^3C_2(100)(4)^2 - ^3C_3(4)^3\)
=\((100)^3-3(100)^2(4)+3(100)(4)^2-(4)^3\)
=\(1000000-120000+4800-64\)
= \(884736\)
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