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

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) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is 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 Number Second Number Sum
1 -15 1+(-15)=-14
3 -5 3+(-5)=-2
-1 15 -1+15=14
-3 5 -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 , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

------------------------------------------------------------

Answer:
So factors to
Answer by scott8148(6628) (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)
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