SOLUTION: Hello, thank you much for taking your time to help me! It's much appreciated. I need help factoring an equation. I know the original equation and I know it's factored answer.

Question 407874: Hello, thank you much for taking your time to help me! It's much appreciated.
I need help factoring an equation.
I know the original equation and I know it's factored answer.
The part that I can't understand is how to get there.
The equation is: 6a^2 - 9ab - 15b^2
The answer is: 3(2a - 5b)(a + b)
When I factor it, I reach: 3(2a^2 - 3ab - 5b^2)
Where do I go from here? How do I do it? Why do I do it that way?
Any help is beyond loved!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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

Looking at we can see that the first term is and the last term is where the coefficients are 2 and -5 respectively.

Now multiply the first coefficient 2 and the last coefficient -5 to get -10. Now what two numbers multiply to -10 and add to the middle coefficient -3? Let's list all of the factors of -10:

Factors of -10:
1,2,5,10

-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -10
(1)*(-10)
(2)*(-5)
(-1)*(10)
(-2)*(5)

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

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

First Number	Second Number	Sum
1	-10	1+(-10)=-9
2	-5	2+(-5)=-3
-1	10	-1+10=9
-2	5	-2+5=3

From this list we can see that 2 and -5 add up to -3 and multiply to -10

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 )

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

So our expression goes from and factors further to

------------------
Answer:

So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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