# How do you multiply (x+1)^3?

Jun 13, 2018

${\left(x + 1\right)}^{3} = {x}^{3} + 3 {x}^{2} + 3 x + 1$

#### Explanation:

The Binomial Theorem in one variable states that:

(1+x)^n = sum_(k=0)^n ""^nC_k * x^k

In this example $n = 3$

$\therefore {\left(1 + x\right)}^{3} = {\text{^3C_0 x^0 + ""^3C_1 x^1 + ""^3C_2 x^2 + }}^{3} {C}_{3} {x}^{3}$

$= 1 + 3 x + \frac{3 \times 2}{2 \times 1} {x}^{2} + {x}^{3}$

$= 1 + 3 x + 3 {x}^{2} + {x}^{3}$

Rewriting terms in the order of the original question:

${\left(x + 1\right)}^{3} = {x}^{3} + 3 {x}^{2} + 3 x + 1$