# How do you factor the expression 9x^2 - 4?

Dec 16, 2015

$\left(3 x - 2\right) \left(3 x + 2\right)$

#### Explanation:

Given: $9 {x}^{2} - 4$

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This is very similar to $\left({a}^{2} - {b}^{2}\right)$ which can be factored into
$\left(a - b\right) \left(a + b\right)$. So if we can change $9 {x}^{2} - 4$ into the standard form of $\left({a}^{2} - {b}^{2}\right)$ we have our solution.

Consider $9 {x}^{2}$
This can be written as ${\left(3 x\right)}^{2}$

Consider 4
This can be written as ${2}^{2}$
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Write as ${\left(3 x\right)}^{2} - {2}^{2}$ when factored this becomes:

$\left(3 x - 2\right) \left(3 x + 2\right)$