SOLUTION: group factoring x^3y^3+5x^2y^3+2x^3+10x^2

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Question 215242: group factoring
x^3y^3+5x^2y^3+2x^3+10x^2
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Factor by grouping:

Whenever you factor, you should start by factoring out the Greatest Common Factors (GCF) of the entire expression (if it is not 1). Since this expression has a GCF of , we'll start by factoring it out:

To factor by grouping
  1. Rewrite the expression as additions (so you can use the Commutative and Associative Properties to rearrange and regroup the expression as you choose).
  2. Find sets of terms with a GCF (possibly by rearranging the terms), group them together and factor out the GCF from each group.
  3. If the "non-GCF" factor of each group matches and you can then factor this out from each group and you are done.
  4. If the "non-GCF" factor does not match,
    • Are they negatives of each other? If so, then factor out a (-1) from one of them and this will make them match and you can then factor them out.
    • If they are not negatives of each other, then return to step #2 and try rearranging and regrouping into different groups to see if you can factor those. (Remember, not every expression will factor by grouping. So you may eventually run out of possible regroupings without being able to factor any of them.)

Now let's apply this to the second factor of:

Step #1: The expression is already all additions.
Step #2: Since the first two terms have a GCF of and the last two terms have a GCF of 2, we'll try factoring without having to rearrange anything. Factoring out from the first two terms and 2 from the last two terms we get:

Step #3: The "non-GCF" factor of both groups is . We are lucky because it is the same for both groups and we can factor it out of each group. (If it was not the same, then we would have more work (Step #4 above) to do.) Factoring out from each group we get:

Since none of these three factors will factor any further, we are finished factoring. We can, if we choose, use the Associative Property to remove the "extra" parentheses:
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