# What is the standard form of y= (x+2) (4x+1) ?

Dec 5, 2015

$y = 4 {x}^{2} + 9 x + 2$

#### Explanation:

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

Given $y = \left(x + 2\right) \left(4 x + 1\right)$
we can convert this into standard form by simply multiplying the two factors on the right side:
$\textcolor{w h i t e}{\text{XXX}} \left(x + 2\right) \left(4 x + 1\right) = 4 {x}^{2} + 9 x + 2$

Dec 5, 2015

$y = 4 {x}^{2} + 9 x + 2$

#### Explanation:

$y = \left(x + 2\right) \left(4 x + 1\right)$

Foil the two binomials.

$a = x , b = 2 , c = 4 x , d = 1$

$y = \left(x \cdot 4 x\right) + \left(x \cdot 1\right) + \left(2 \cdot 4 x\right) + \left(2 \cdot 1\right)$

Simplify.

$y = 4 {x}^{2} + x + 8 x + 2$

Combine like terms.

$y = 4 {x}^{2} + 9 x + 2$