# What is the standard form of  y= (x+3)(x-3)^2 ?

Mar 29, 2016

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

#### Explanation:

Breaking it down into parts.

$\textcolor{b r o w n}{\text{Step 1} \to}$ consider ${\left(x - 3\right)}^{2}$

This is $\textcolor{m a \ge n t a}{\left(x - 3\right)} \textcolor{b l u e}{\left(x - 3\right)}$

This gives;color(magenta)(" "xcolor(blue)((x-3)) -3color(blue)((x-3))

${x}^{2} - 3 x - 3 x + 9 \text{ "=" } {x}^{2} - 6 x + 9$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Step 2} \to}$ Now we have $\textcolor{m a \ge n t a}{\left(x + 3\right)} \textcolor{b l u e}{\left({x}^{2} - 6 x + 9\right)}$

This is $\textcolor{b l u e}{{x}^{2} \textcolor{m a \ge n t a}{\left(x + 3\right)} - 6 x \textcolor{m a \ge n t a}{\left(x + 3\right)} + 9 \textcolor{m a \ge n t a}{\left(x + 3\right)}}$

${x}^{3} + 3 {x}^{2} - 6 {x}^{2} - 18 x + 9 x + 27$

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