SOLUTION: Factoring a^2 - 8ab/3 - b^2

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Question 706400: Factoring a^2 - 8ab/3 - b^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2-8ab%2F3-b%5E2
The fraction makes the factoring more difficult. So we will start by factoring out 1/3:
%281%2F3%29%283a%5E2-8ab-3b%5E2%29
If you haven't factored out a fraction like this before, then take a moment to make sure you understand how it works. Notice how, if you use the Distributive Property to multiply this out you end up back where you started. And you may also notice how much easier it is to finish the factoring with the fraction out of the way.

It should not take long to figure out out to factor the trinomial:
%281%2F3%29%283a%2Bb%29%28a-3b%29
This should be an acceptable answer.

If you don't like having the factor of 1/3 you could use the Distributive Property again. Just use it once to multiply the 1/3 by either of the other factors. So you could get:
%28a%2Bb%2F3%29%28a-3b%29 if you multiply the 3a+b by 1/3; or
%283a%2Bb%29%28a%2F3-b%29 if you multiply the a-3b by 1/3