SOLUTION: please show me how to factor a polynomial completely thank you -36a2b+21ab2-3b3

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Question 183921: please show me how to factor a polynomial completely thank you

-36a2b+21ab2-3b3

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor completely: Note: You can indicate exponents by use of the caret symbol (^). Example - a-squared would look like a^2
-36a%5E2b%2B21ab%5E2-3b%5E3 First factor out those factors that are common to each term, in this case, I would factor out -3b thus:
-3b%2812a%5E2-7ab%2Bb%5E2%29 Notice the change of sign on each factor when you factor the -3.
Now to factor the trinomial in parentheses, first look at the leading term, (12a%5E2), and note that this can be factored as:
12a%5E2+=+1%2A12%2Aa%2Aa or -1%2A-12%2Aa%2Aa
12a%5E2+=+2%2A6%2Aa%2Aa or -2%2A-6%2Aa%2Aa
12a%5E2+=+3%2A4%2Aa%2Aa or highlight%28-3%2A-4%2Aa%2Aa%29
Now notice the middle term, -7ab The only way to factor this is:
-7ab+=+-7%2Aa%2Ab and you can get -7 by adding highlight%28-3%2B%28-4%29%29 and the last term b%5E2 can only be factored as highlight%28b%2Ab%29
So putting it all together, you get:
-36a%5E2b%2B21ab%5E2-3b%5E3+=+highlight%28-3b%283a-b%29%284a-b%29%29