SOLUTION: HELP Factor 9a^2-4b^2+12bc-9c^2 THANK YOU FOR ANGELS LIKE YOU

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: HELP Factor 9a^2-4b^2+12bc-9c^2 THANK YOU FOR ANGELS LIKE YOU      Log On


   

Question 184769: HELP
Factor
9a^2-4b^2+12bc-9c^2
THANK YOU FOR ANGELS LIKE YOU
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9a%5E2-4b%5E2%2B12bc-9c%5E2 Start with the given expression


9a%5E2-%284b%5E2-12bc%2B9c%5E2%29 Factor a negative 1 from 4b%5E2%2B12bc-9c%5E2 to get -%284b%5E2-12bc%2B9c%5E2%29


9a%5E2-%282b-3c%29%5E2 Factor 4b%5E2-12bc%2B9c%5E2 to get %282b-3c%29%5E2. Note: this is a perfect square. Let me know if you need me to elaborate on how I factored this.


%283a%29%5E2-%282b-3c%29%5E2 Rewrite 9a%5E2 as %283a%29%5E2



Let x=3a and y=2b-3c


x%5E2-y%5E2 Replace "3a" with "x" and 2b-3c with "y"



Now we have a difference of squares, which factors to


%28x%2By%29%28x-y%29


%283a%2B2b-3c%29%283a-%282b-3c%29%29 Plug in x=3a and y=2b-3c


%283a%2B2b-3c%29%283a-2b%2B3c%29 Distribute



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Answer:


So 9a%5E2-4b%5E2%2B12bc-9c%5E2 completely factors to %283a%2B2b-3c%29%283a-2b%2B3c%29


In other words, 9a%5E2-4b%5E2%2B12bc-9c%5E2=%283a%2B2b-3c%29%283a-2b%2B3c%29