# What is the standard form of  y= (x + 3)(x + 4) ?

Dec 16, 2015

$y = {x}^{2} + 7 x + 12$

#### Explanation:

A polynomial is in standard form if it is written with all the ${x}^{2}$, $x$, and constant terms together.

It's typically written as

$y = a {x}^{2} + b x + c$

where $a , b ,$ and $c$ are all constants that can vary.

Standard form is useful because it generalizes how to find the roots of any quadratic equation through the quadratic formula (x=(-b+-sqrt(b^2-4ac))/(2a).

In your case, to find the standard version of the equation, distribute the two binomials through the " FOIL " method.

FOIL stands for F irst, O uter, I nner, L ast. These are the four different combinations of terms you can multiply when you have two binomials.

First: multiply the first term in each binomial
$\left(\textcolor{red}{x} + 3\right) \left(\textcolor{red}{x} + 4\right)$
$= {x}^{2}$

Outer: multiply the terms on the outside
$\left(\textcolor{red}{x} + 3\right) \left(x + \textcolor{red}{4}\right)$
$= 4 x$

Inner: multiply the terms on the inside
$\left(x + \textcolor{red}{3}\right) \left(\textcolor{red}{x} + 4\right)$
$= 3 x$

Last: multiply the last term in each binomial
$\left(x + \textcolor{red}{3}\right) \left(x + \textcolor{red}{4}\right)$
$= 12$

Now, add all the different products.

$y = {x}^{2} + 4 x + 3 x + 12$

Combine like terms.

$y = {x}^{2} + 7 x + 12$

This is in the standard form of the quadratic equation $y = a {x}^{2} + b x + c$, where $a = 1 , b = 7 , c = 12$.