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

Dec 1, 2015

$y = {x}^{2} + 7 x + 10$

#### Explanation:

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

Dec 1, 2015

$y = {x}^{2} + 7 x + 10$
Look at the method. It is using something called the 'Distributive' law

#### Explanation:

Given $y = \left(\textcolor{g r e e n}{x} \textcolor{red}{+} \textcolor{b l u e}{2}\right) \left(x + 5\right)$

$y = \textcolor{g r e e n}{x} \left(x + 5\right) \textcolor{red}{+} \textcolor{b l u e}{2} \left(x + 5\right)$

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Notice that the sign of the $\textcolor{b l u e}{2}$ follows it.
If the sign had been negative then we would have $\textcolor{red}{-} \textcolor{b l u e}{2} \left(x + 5\right)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$y = \left(\textcolor{g r e e n}{x} \times x\right) + \left(\textcolor{g r e e n}{x} \times 5\right) \textcolor{w h i t e}{\ldots .} + \textcolor{w h i t e}{\ldots .} \left(\textcolor{b l u e}{2} \times x\right) + \left(\textcolor{b l u e}{2} \times 5\right)$

$y = {x}^{2} + 5 x + 2 x + 10$

$y = {x}^{2} + 7 x + 10$