How do you factor completely $18m^2-8$ ?

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Answer 1 · 2016-10-28T21:03:48

$18m^2-8 = 2(3m-2)(3m+2)$

The difference of squares identity can be written:

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

In our example, we use this with $a=3m$ and $b=2$ after separating out the common scalar factor $2$ , as follows:

$18m^2-8 = 2(9m^2-4)$

$color(white)(18m^2-8) = 2(9m^2-4)$

$color(white)(18m^2-8) = 2((3m)^2-2^2)$

$color(white)(18m^2-8) = 2(3m-2)(3m+2)$

How do you factor completely 18m^2-818m^2-8?