# How do you factor 4a^3-64a?

May 7, 2016

$4 a \left(a - 4\right) \left(a + 4\right)$

#### Explanation:

4 is a factor of both 4 and 64

$a$ is a factor of both $4 {a}^{2} \text{ and } 64 a$

Factor out $4 a$ giving:

$4 a \left({a}^{2} - 16\right)$

But 16 is the same as ${4}^{2}$

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

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compare to the example ${y}^{2} - {z}^{2} = \left(y - z\right) \left(y + z\right)$
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color(brown)(4a(a^2-4^2))color(blue)(" "->" "4a(a-4)(a+4)