SOLUTION: The signs keep messing me up on this type of question. 64x^3-27/4x^2-36 times 4x+12/64x^2+48+36 Answer: 4x-3/4(x-3)

Algebra ->  Test -> SOLUTION: The signs keep messing me up on this type of question. 64x^3-27/4x^2-36 times 4x+12/64x^2+48+36 Answer: 4x-3/4(x-3)      Log On


   

Question 370372: The signs keep messing me up on this type of question.
64x^3-27/4x^2-36 times 4x+12/64x^2+48+36
Answer: 4x-3/4(x-3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2864x%5E3-27%29%2F%284x%5E2-36%29%29%2A%28%284x%2B12%29%2F%2864x%5E2%2B48x%2B36%29%29
Long ago, when you first learned how to multiply fractions, you probably learned that you could cancel common factors, even between the two fractions, before you multiplied and that doing so made the problem easier. This is still true. The main difference is that the factoring is not as easy. So we will start by factoring each numerator and denominator.

The first numerator is a difference of cubes for which we have the pattern, a%5E3-b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29, to use when factoring. The other numerator and the two denominators have a Greatest Common Factor (GCF) to factor out:

The first denominator now has a factor that is a difference of squares for which we have the pattern, a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29, to use when factoring:

Now we can see several factors which will cancel:

leaving:
%28%284x-3%29%2F%284%28x-3%29%29%29%2A%281%2F1%29%29%29%29
which simplifies to:
%284x-3%29%2F%284%28x-3%29%29