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

Question

Using binomial evaluate the following:

$(96)^3$

✓

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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