# What is the standard form of y= (x+6)(x-3)(x+2)?

Apr 23, 2017

See the entire solution process below:

#### Explanation:

First, multiply the two right most terms within parenthesis. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = \left(x + 6\right) \left(\textcolor{red}{x} - \textcolor{red}{3}\right) \left(\textcolor{b l u e}{x} + \textcolor{b l u e}{2}\right)$ becomes:

$y = \left(x + 6\right) \left(\left(\textcolor{red}{x} \times \textcolor{b l u e}{x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{2}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{x}\right) - \left(\textcolor{red}{3} \times \textcolor{b l u e}{2}\right)\right)$

$y = \left(x + 6\right) \left({x}^{2} + 2 x - 3 x - 6\right)$

We can now combine like terms:

$y = \left(x + 6\right) \left({x}^{2} + \left(2 - 3\right) x - 6\right)$

$y = \left(x + 6\right) \left({x}^{2} + \left(- 1\right) x - 6\right)$

$y = \left(x + 6\right) \left({x}^{2} - 1 x - 6\right)$

Now, we again multiply the two terms in parenthesis on the right side of the equation:

$y = \left(\textcolor{red}{x} + \textcolor{red}{6}\right) \left(\textcolor{b l u e}{{x}^{2}} - \textcolor{b l u e}{1 x} - \textcolor{b l u e}{6}\right)$ becomes:

$y = \left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{1 x}\right) - \left(\textcolor{red}{x} \times \textcolor{b l u e}{6}\right) + \left(\textcolor{red}{6} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{1 x}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{6}\right)$

$y = {x}^{3} - 1 {x}^{2} - 6 x + 6 {x}^{2} - 6 x - 36$

We can group and combine like terms to put the equation into standard form:

$y = {x}^{3} + 6 {x}^{2} - 1 {x}^{2} - 6 x - 6 x - 36$

$y = {x}^{3} + \left(6 - 1\right) {x}^{2} + \left(- 6 - 6\right) x - 36$

$y = {x}^{3} + 5 {x}^{2} + \left(- 12\right) x - 36$

$y = {x}^{3} + 5 {x}^{2} - 12 x - 36$