# What is the standard form of y= (x - 6)(x^2 + 6x + 36) ?

Mar 22, 2017

See the entire solution process below:

#### Explanation:

To multiply these two terms and put it into standard form you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = \left(\textcolor{red}{x} - \textcolor{red}{6}\right) \left(\textcolor{b l u e}{{x}^{2}} + \textcolor{b l u e}{6 x} + \textcolor{b l u e}{36}\right)$ becomes:

$y = \left(\textcolor{red}{x} \times \textcolor{b l u e}{{x}^{2}}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{6 x}\right) + \left(\textcolor{red}{x} \times \textcolor{b l u e}{36}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{{x}^{2}}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{6 x}\right) - \left(\textcolor{red}{6} \times \textcolor{b l u e}{36}\right)$

$y = {x}^{3} + 6 {x}^{2} + 36 x - 6 {x}^{2} - 36 x - 216$

We can now group and combine like terms and put into standard form:

$y = {x}^{3} + 6 {x}^{2} - 6 {x}^{2} + 36 x - 36 x - 216$

$y = {x}^{3} + \left(6 {x}^{2} - 6 {x}^{2}\right) + \left(36 x - 36 x\right) - 216$

$y = {x}^{3} + 0 + 0 - 216$

$y = {x}^{3} - 216$