SOLUTION: Factor completely. b2 – ab – 6a2

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Question 109879: Factor completely. b2 – ab – 6a2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First off, what two numbers multiply to -6 (the last coefficient) but add to -1 (the middle coefficient)? It turns out that -3 and 2 multiply to -6 but add to -1.

So replace the middle term of b%5E2-ab-6a%5E2 with -3ab%2B2ab to get b%5E2-3ab%2B2ab-6a%5E2

Now let's factor b%5E2-3ab%2B2ab-6a%5E2 by grouping


%28b%5E2-3ab%29%2B%282ab-6a%5E2%29 Group like terms


b%28b-3a%29%2B2a%28b-3a%29 Factor out the GCF of b out of the first group. Factor out the GCF of 2a out of the second group


%28b%2B2a%29%28b-3a%29 Since we have a common term of b%2B-3a, we can combine like terms

So b%5E2-3ab%2B2ab-6a%5E2 factors to %28b%2B2a%29%28b-3a%29

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Answer:

This means b%5E2-ab-6a%5E2 factors to %28b%2B2a%29%28b-3a%29 also


Notice how %28b%2B2a%29%28b-3a%29 foils back to b%5E2-3ab%2B2ab-6a%5E2 which simplifies to b%5E2-ab-6a%5E2. So this verifies our answer.