I'm having some trouble factoring a problem.

It's 75x^2 - 27

I know I can first factor out a GCF of 3 which leaves me with 3(25x^2 - 9)

This seems to me to be a differences of squares but I cannot figure out what to do next.

Thank you.

the pattern for the difference of squares is

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

so for your 25x^2 - 9
or
(5x)^2 - (3)^2 , what do you see for a and what for b ?
what would you get as the factors ??

I'm thinking it would be 3(5x-3)(5x+3)?

correct

To factor the expression 75x^2 - 27 completely, you're on the right track by factoring out the greatest common factor (GCF) of 3. This allows you to simplify the problem to 3(25x^2 - 9), as you mentioned.

Now, let's focus on factoring the expression within the parentheses, 25x^2 - 9. This expression is indeed a difference of squares, which means it can be factored further.

The difference of squares formula states that for any expression in the form of a^2 - b^2, it can be factored as (a - b)(a + b).

In our case, we have 25x^2 - 9, which can be viewed as (5x)^2 - 3^2.

So, according to the difference of squares formula, we can represent 25x^2 - 9 as (5x - 3)(5x + 3).

To summarize, the fully factored form of 75x^2 - 27 is 3(5x - 3)(5x + 3).