# How do you factor 2c^2-32d^2?

Mar 12, 2017

$2 \left(c - 4 d\right) \left(c + 4 d\right)$

#### Explanation:

Worth remembering the standard form of $\left({a}^{2} - {b}^{2}\right) = \left(a - b\right) \left(a + b\right)$

IT CROPS UP ALL OVER THE PLACE

We have a version of it in this question!
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So we look for values that we can square

2 is a problem so lets try and 'sort of' move it out of the way

Factor out 2 giving:

$2 \left({c}^{2} - 16 {d}^{2}\right)$

Now we are getting somewhere. The 16 can be written as ${4}^{2}$ and we are looking for squared values

Write as:

$2 \left({c}^{2} - {\left(4 d\right)}^{2}\right)$

So using the standard form of ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$ we write:

$2 \left({c}^{2} - {\left(4 d\right)}^{2}\right) \text{ } = 2 \left(c - 4 d\right) \left(c + 4 d\right)$