Question

Evaluate (999)^3. Find this answer​

Answer 1

$\large\mathtt{997,002,999}$

Method :

Solved using binomial theorem.

Given :

${(999)}^3$

Solution :

$\implies {(999)}^{3}$

$\implies {(1000-1)}^{3}$

$\text{General Form of binomial equation :}$

$\color{purple}{{(x-a)}^{3}=3C_0{x}^{3}-3C_1{x}^2a+3C_2x{a}^2-3C_3a^3}$

$x=1000,a=1$

$\mathtt{\implies 3C_0(1000)^3-3C_1(1000)^2(1)+3C_2(1000)(1)^2-3C_3(1)^3}$

$\mathtt{\implies(1000000000)-3(1000000)+\frac{3\times2}{1\times2}(1000)-1}$

$\mathtt{\implies 1000000000-3(1000000)+3(1000)-1}$

$\mathtt{\implies 1000000000-3000000+3000-1}$

$\mathtt{\implies 997,002,999}$