Using Binomial Theorem, evaluate (96)3
Question:

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

Solution:

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

$\therefore(96)^{3}=(100-4)^{3}$

$={ }^{3} \mathrm{C}_{0}(100)^{3}-{ }^{3} \mathrm{C}_{1}(100)^{2}(4)+{ }^{3} \mathrm{C}_{2}(100)(4)^{2}-{ }^{3} \mathrm{C}_{3}(4)^{3}$

$=(100)^{3}-3(100)^{2}(4)+3(100)(4)^{2}-(4)^{3}$

$=1000000-120000+4800-64$

$=884736$

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