Question

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

Answer 1

\(96 \) 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, \(96 = 100 - 4\)
∴ \((96)^3=(100-4)^3\)
=\(^3C_0(100)^3 - ^3C_1(100)^2(4)+ ^3C_2(100)(4)^2 - ^3C_3(4)^3\)
=\((100)^3-3(100)^2(4)+3(100)(4)^2-(4)^3\)
=\(1000000-120000+4800-64\)
= \(884736\)