# What is the standard form of y=(3x+4)(x/2-5) ?

May 27, 2017

See a solution process below:

#### Explanation:

To find convert this equation to the standard form we need to multiply the two terms on the right. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = \left(\textcolor{red}{3 x} + \textcolor{red}{4}\right) \left(\textcolor{b l u e}{\frac{x}{2}} - \textcolor{b l u e}{5}\right)$ becomes:

$y = \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{\frac{x}{2}}\right) - \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{5}\right) + \left(\textcolor{red}{4} \times \textcolor{b l u e}{\frac{x}{2}}\right) - \left(\textcolor{red}{4} \times \textcolor{b l u e}{5}\right)$

$y = \frac{3}{2} {x}^{2} - 15 x + 2 x - 20$

We can now combine like terms:

$y = \frac{3}{2} {x}^{2} + \left(- 15 + 2\right) x - 20$

$y = \frac{3}{2} {x}^{2} + \left(- 13\right) x - 20$

$y = \frac{3}{2} {x}^{2} - 13 x - 20$