What is the standard form of  y= (2x-9)(x-5)-(2x+7)^2?

Dec 10, 2015

$y = - 2 {x}^{2} - 47 x - 4$

Explanation:

The general standard form for a quadratic is
$\textcolor{w h i t e}{\text{XXX}} y = a {x}^{2} + b x + c$
with constants $a , b , c$

Given
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{\left(2 x - 9\right) \left(x - 5\right)} - \textcolor{b l u e}{{\left(2 x + 7\right)}^{2}}$

Expanding the terms:
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{\left(2 {x}^{2} - 19 x + 45\right)} - \textcolor{b l u e}{\left(4 {x}^{2} + 28 x + 49\right)}$

Combine like terms:
$\textcolor{w h i t e}{\text{XXX}} y = - 2 {x}^{2} - 47 x - 4$