Question

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

Answer 1

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

Explanation:

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)`