Using binomial evaluate the following: (96)^3 - Vidyadip

Question

Using binomial evaluate the following:
$(96)^3$

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Answer

We have,
$(96)^3=(100-4)^3$
$={^3\text{C}}_0\times100^3+{^3\text{C}}_1\times100^2\times(-4)+{^3\text{C}}_2\times100\times(-4)^2+{^3\text{C}}_3\times(-4)^3$
$=100^3-3\times100^2\times4+3\times100\times4^2-4^3$
$=1000000-120000+4800-64$
$1004800-120064$
$=884736$
$\therefore(96)^3=884736$

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