# What is the standard form of y=(x + 3)^3 ?

Apr 30, 2017

${x}^{3} + 9 {x}^{2} + 27 x + 27$

#### Explanation:

$\text{Given " (x+a)(x+b)(x+c)" the expansion is}$

$= {x}^{3} + \left(a + b + c\right) {x}^{2} + \left(a b + b c + a c\right) x + a b c$

$\text{now } {\left(x + 3\right)}^{3} = \left(x + 3\right) \left(x + 3\right) \left(x + 3\right)$

$\text{with } a = b = c = 3$

$\Rightarrow {\left(x + 3\right)}^{3}$

$= {x}^{3} + \left(3 + 3 + 3\right) {x}^{2} + \left(9 + 9 + 9\right) x + \left(3 \times 3 \times 3 \times 3\right)$

$= {x}^{3} + 9 {x}^{2} + 27 x + 27$

Apr 30, 2017

$\textcolor{b l u e}{y = {x}^{3} + 9 {x}^{2} + 27 x + 27}$

#### Explanation:

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

$\textcolor{w h i t e}{\ldots \ldots \ldots .} x + 3$
$\textcolor{w h i t e}{\ldots \ldots} \times x + 3$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \overline{{x}^{2} + 3 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots . .} + 3 x + 9$
$\textcolor{w h i t e}{\ldots \ldots \ldots . .} \overline{{x}^{2} + 6 x + 9}$
$\textcolor{w h i t e}{\ldots \ldots .} \times x + 3$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \overline{{x}^{3} + 6 {x}^{2} + 9 x}$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots .} 3 {x}^{2} + 18 x + 27$
color(white)(.............)overline(color(blue)(x^3+9x^2+27x+27)