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.

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

$=3_{C_0}(100{)}^3-3_{C_1}(100{)}^2\left(4\right)+3_{C_2}\left(100\right)(4{)}^2-3_{C_3}(4{)}^3$

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

$=884736$