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

Jun 21, 2018

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

#### Explanation:

the standard form of a second-degree polynomial function should look like this

color(green)(y=ax^2+bx+c

so we try to reach that for with your function

$y = \left(x + 3\right) \left(x + 4\right)$

Using the Distributive property

$y = x \left(x + 4\right) + 3 \left(x + 4\right)$

$y = x \cdot x + x \cdot 4 + 3 \cdot x + 3 \cdot 4$

Multiply

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

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

Jun 21, 2018

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

#### Explanation:

$y = \left(x + 3\right) \left(x + 4\right)$

The standard form of a quadratic equation is $a {x}^{2} + b x + c$. To make this equation in standard form, we expand/simplify this using FOIL:

Following this image, we can multiply it out.

The $\textcolor{t e a l}{\text{firsts}}$:
$\textcolor{t e a l}{x \cdot x} = {x}^{2}$

The $\textcolor{\in \mathrm{di} g o}{\text{outers}}$:
$\textcolor{\in \mathrm{di} g o}{x \cdot 4} = 4 x$

The $\textcolor{p e r u}{\text{inners}}$:
$\textcolor{p e r u}{3 \cdot x} = 3 x$

The $\textcolor{o l i v e \mathrm{dr} a b}{\text{lasts}}$:
$\textcolor{o l i v e \mathrm{dr} a b}{3 \cdot 4} = 12$

Combine them all together to get:
${x}^{2} + 4 x + 3 x + 12$

We can still combine the like terms $\textcolor{b l u e}{4 x}$ and $\textcolor{b l u e}{3 x}$:
${x}^{2} + 7 x + 12$

As you can see, this matches the form $a {x}^{2} + b x + c$. Therefore, the quadratic equation in standard form is ${x}^{2} + 7 x + 12$.

Hope this helps!

Jun 21, 2018

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

#### Explanation:

$\text{the standard form of a quadratic is }$

•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0

$\text{expanding the factors gives}$

$y = {x}^{2} + 7 x + 12 \leftarrow \textcolor{red}{\text{in standard form}}$