# What is the standard form of  y= (3x-5)(2x+12)-7x^2+15x?

Oct 23, 2017

See a solution process below:

#### Explanation:

First, multiply the two terms in parenthesis by multiplying each individual term in the left parenthesis by each individual term in the right parenthesis.

$y = \left(\textcolor{red}{3 x} - \textcolor{red}{5}\right) \left(\textcolor{b l u e}{2 x} + \textcolor{b l u e}{12}\right) - 7 {x}^{2} + 15 x$ becomes:

$y = \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{2 x}\right) + \left(\textcolor{red}{3 x} \times \textcolor{b l u e}{12}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{2 x}\right) - \left(\textcolor{red}{5} \times \textcolor{b l u e}{12}\right) - 7 {x}^{2} + 15 x$

$y = 6 {x}^{2} + 36 x - 10 x - 60 - 7 {x}^{2} + 15 x$

We can now group and combine like terms:

$y = 6 {x}^{2} - 7 {x}^{2} + 36 x - 10 x + 15 x - 60$

$y = \left(6 - 7\right) {x}^{2} + \left(36 - 10 + 15\right) x - 60$

$y = - 1 {x}^{2} + 41 x - 60$

$y = - {x}^{2} + 41 x - 60$