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

Mar 28, 2018

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

#### Explanation:

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

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

Mar 28, 2018

color(magenta)(x^3+3x^2+3x+1

#### Explanation:

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{x + 1}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$${x}^{2} + x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a}$$+ x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{{x}^{2} + 2 x + 1}$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{{x}^{3} + 2 {x}^{2} + x}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a}$${x}^{2} + 2 x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{{x}^{3} + 3 {x}^{2} + 3 x + 1}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$color(magenta)(x^3+3x^2+3x+1