SOLUTION: How do you factor a^2 - 2ab - 15b^2 completly, whats the answer?

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Question 150639: How do you factor a^2 - 2ab - 15b^2 completly, whats the answer?
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at 1a%5E2-2ab-15b%5E2 we can see that the first term is 1a%5E2 and the last term is -15b%5E2 where the coefficients are 1 and -15 respectively.

Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient -2? Let's list all of the factors of -15:



Factors of -15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -2

First NumberSecond NumberSum
1-151+(-15)=-14
3-53+(-5)=-2
-115-1+15=14
-35-3+5=2



From this list we can see that 3 and -5 add up to -2 and multiply to -15


Now looking at the expression 1a%5E2-2ab-15b%5E2, replace -2ab with 3ab%2B-5ab (notice 3ab%2B-5ab adds up to -2ab. So it is equivalent to -2ab)

1a%5E2%2Bhighlight%283ab%2B-5ab%29%2B-15b%5E2


Now let's factor 1a%5E2%2B3ab-5ab-15b%5E2 by grouping:


%281a%5E2%2B3ab%29%2B%28-5ab-15b%5E2%29 Group like terms


a%28a%2B3b%29-5b%28a%2B3b%29 Factor out the GCF of a out of the first group. Factor out the GCF of -5b out of the second group


%28a-5b%29%28a%2B3b%29 Since we have a common term of a%2B3b, we can combine like terms

So 1a%5E2%2B3ab-5ab-15b%5E2 factors to %28a-5b%29%28a%2B3b%29


So this also means that 1a%5E2-2ab-15b%5E2 factors to %28a-5b%29%28a%2B3b%29 (since 1a%5E2-2ab-15b%5E2 is equivalent to 1a%5E2%2B3ab-5ab-15b%5E2)



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Answer:
So a%5E2-2ab-15b%5E2 factors to %28a-5b%29%28a%2B3b%29

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
factors of -15 that "combine" to -2

like 3 and -5

(a+3b)(a-5b)