Question

How do you use the binomial formula to expand ${(x+1)}^3$?

Answer 1

$x^3+3x^2+3x+1$

Explanation:

Binomial formula for ${(a+b)}^3$

$\Rightarrow {}^3{C}_0{a}^3{b}^0+{}^3{C}_1{a}^2{b}^1+{}^3{C}_2{a}^1{b}^2+{}^3{C}_3{a}^0{b}^3$

Here a = x and b = 1

$\Rightarrow {}^3{C}_0{x}^3+{}^3{C}_1{x}^2\times 1+{}^3{C}_2{x}^1\times 1+{}^3{C}_3\times 1$

As $\to {}^3{C}_0={}^3{C}_3=1$ and $\to {}^3{C}_1={}^3{C}_2=2$

$\Rightarrow x^3+3x^2+3x+1$