SOLUTION: Find the greatest common factor for each of the following sets of terms. 12a^3b^2, 18a^2b^3, 6a^4b^4

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Question 77423: Find the greatest common factor for each of the following sets of terms.
12a^3b^2, 18a^2b^3, 6a^4b^4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can see the GCF among the numbers is the greatest number that can go into 12,18,and 6. This number is 6 since it can go into all 3 of these numbers. Now we need to look at the variables. We see that they all have a and b in their terms, so our GCF will have at least one of each. Since the lowest exponent for a is 2, our GCF for a is a%5E2. Since the lowest exponent for b is 2, the GCF for b is b%5E2. Combining all of this info, we get:
GCF:
6a%5E2b%5E2
Notice how we can factor out the GCF out of all of these evenly. For instance, say we have

12a%5E3b%5E2%2B18a%5E2b%5E3%2B6a%5E4b%5E4
We can factor the GCF out of the expression to get
6a%5E2b%5E2%282a%2B3b%2Ba%5E2b%5E2%29
When we distribute 6a%5E2b%5E2 to the terms in the parenthesis we get
12a%5E3b%5E2%2B18a%5E2b%5E3%2B6a%5E4b%5E4 again