Factor the expression.
27w^2-12
I don't have an answer, I don't understand the steps can someone show me the correct steps for this problem, and then I can solve it?
3(9w^2-4) = 3(3w-2)(3w+2)
Thanks so much PsyDAG! :)
Welcome
To factor the expression 27w^2 - 12, we need to find two numbers that multiply together to give 27w^2 and add up to give -12.
First, let's look at the coefficient of w^2, which is 27. We can break it down into its prime factors: 3 * 3 * 3 = 27.
Next, we look at the constant term, which is -12. We can break it down into its prime factors: 2 * 2 * 3 = 12.
Now, let's see if we can rearrange the factors in a way that will help us find the correct combination. Since we need to find two numbers that add up to give -12, and the prime factorization of 12 contains a 3, it makes sense to split the 27w^2 term into 9w^2 and 3w^2.
Now we have: 9w^2 - 3w^2 - 12.
To factor this expression, we can take out the greatest common factor (GCF) from each term, which is 3w^2:
3w^2(3 - 1) - 12.
Simplifying further, we get:
3w^2(2) - 12.
Finally, we can factor out the common factor of 2:
2(3w^2 - 6).
So, the factored form of the expression 27w^2 - 12 is 2(3w^2 - 6).