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

Dec 5, 2015

The standard form is $y = - {x}^{2} + 5 x - 12$.

Explanation:

$y = \left(x + 4\right) \left(2 x - 3\right) - 3 {x}^{2}$

The standard form for a quadratic equation is $a {x}^{2} + b x + c$, where $a , b , \mathmr{and} c$ are coefficients.

First Foil the two binomials.

$\left(x + 4\right) \left(2 x - 3\right)$

$a = x , b = 4 , c = 2 x , d = - 3$

$\left(x + 4\right) \left(2 x - 3\right) = a c + a d + b c + b d$

$\left(x + 4\right) \left(2 x - 3\right) = \left(x \cdot 2 x\right) + \left(x \cdot - 3\right) + \left(4 \cdot 2 x\right) + \left(4 \cdot - 3\right)$

$\left(x + 4\right) \left(2 x - 3\right) = \left(2 {x}^{2}\right) + \left(- 3 x\right) + \left(8 x\right) + \left(- 12\right)$

Combine like terms.

$\left(x + 4\right) \left(2 x - 3\right) = 2 {x}^{2} + 5 x - 12$

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