# How do you factor 8z^2-64?

Mar 29, 2017

See the entire solution process below:

#### Explanation:

$8$ is a common factor for both terms. Therefore, we can rewrite this expression as:

$8 {z}^{2} - 64 \to \left(8 \cdot {z}^{2}\right) - \left(8 \cdot 8\right) \to 8 \left({z}^{2} - 8\right)$

If necessary we can further factor the term: ${z}^{2} - 8$.

We can use this rule to factor this term:

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

We can let ${a}^{2} = {z}^{2}$ therefore $a = z$

We can let ${b}^{2} = 8$ therefore $b = \sqrt{8}$

Substituting gives:

8(z^2 - 8) = 8(z + sqrt(8))(z - sqrt(8)