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

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Answer 1 · 2017-03-29T01:30:07

See the entire solution process below:

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

#8z^2 - 64 -> (8 * z^2) - (8 * 8) -> 8(z^2 - 8)#

If necessary we can further factor the term: #z^2 - 8#.

We can use this rule to factor this term:

#a^2 - b^2 = (a + b)(a - b)#

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)#