Question

I can't seem to factor this completely: 36x^2y-100y^3

Answer 1

Factor a common factor out first.
What is the GCF of 36 and 100?
What is the GCF of x^2y and y^3?

Answer 2

GCF = 4. And Y, for the second bit?

Answer 3

Good. The common factor between both terms is 4y.
Now let's factor that out. What do you get?

Answer 4

OK. 9x^2-25? With the 4y outside of that equation? So 4y(9x^2-25)?

Answer 5

Great.
Now look at 9x^2 - 25. You have two terms, and each is a perfect square. Does this remind you of a binomial you know how to factor? A difference of two squares?

Answer 6

(3x-5y)(3x+5y)?

Answer 7

Correct. Now remember that you had a 4y factor already out, so what is the complete factorization?

Answer 8

4y(3x-5y)(3x+5y)

Answer 9

Great job. Apparently, you were able to factor it.

Answer 10

I can't thank you enough. Seriously. You're an absolute star.

Answer 11

To factor follow these rules:
1. Try to factor a common factor.
2. Factor according to number of terms:
(a) Two terms - try difference of squares, or sum or difference of cubes.
(b) Three terms - try trinomials of form x^2 + bx + c or ax^2 + bx + c
(c) Four terms - try factoring by parts
3. After factoring, look at every factor and try factoring again.
4. Factoring means factoring completely, so a factor may need to be factored again.

Answer 12

You're welcome. Read summary of factoring above. It may come in handy.

Answer 13

I'm about to write it down right now. Once again, thanks a lot for the help AND taking the time to type up those rules. You've been extremely helpful.

Answer 14

No problem at all. Any time. You're welcome.