# What is the standard form of y= (5x + 2)(6x+8) ?

Dec 12, 2015

$y = 30 {x}^{2} + 52 x + 16$

#### Explanation:

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

The given form: $y = \left(5 x + 2\right) \left(6 x + 8\right)$
can easily be converted to this standard form by multiplying the factors on the right side.

There are several ways that the multiplication can be done:

Using the Distributive Property
$\left(5 x + 2\right) \left(6 x + 8\right)$
$\textcolor{w h i t e}{\text{XXX}} = 5 x \left(6 x + 8\right) + 2 \left(6 x + 8\right)$
$\textcolor{w h i t e}{\text{XXX}} = \left(30 {x}^{2} + 40 x\right) + \left(12 x + 16\right)$
(then combining like terms:)
$\textcolor{w h i t e}{\text{XXX}} 30 {x}^{2} + 52 x + 16$

$\text{------------------------------------------------------------------------}$

FOIL
color(white)("XX"){: (color(red)("Multiply"),,), ("First terms:", 5x xx 6x, = 30x^2), ("Outside terms:", 5x xx 8, =40x), ("Inside terms:",2 xx 6x, = 12x), ("Last terms:", 2 xx 8, =16), (color(red)("Add"),,), (,,color(blue)(30x^2+52x+16)) :}

$\text{------------------------------------------------------------------------}$

Tabular Multiplication
{: (xx,"|",5x,+2), ("----",,"----","----"), (6x,"|",color(orange)(30x^2),color(green)(+12x)), (+8,"|",color(green)(40x),color(cyan)(+16)), ("----","----","----","----"), (,color(orange)(30x^2),color(green)(+52x),color(cyan)(+16)) :}