SOLUTION: If {{{a-b=-6}}} and {{{b+c=9}}}, find the value of {{{3a^2-b^2-2c^2}}}.

Algebra ->  Expressions-with-variables -> SOLUTION: If {{{a-b=-6}}} and {{{b+c=9}}}, find the value of {{{3a^2-b^2-2c^2}}}.      Log On


   

Question 1199499: If a-b=-6 and b%2Bc=9, find the value of 3a%5E2-b%5E2-2c%5E2.
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
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If a-b = -6 and b+c = 9, find the value of 3a%5E2-b%5E2-2c%5E2.
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Then a = -6 + b,  c = 9 - b,


      3a^2 - b^2 - 2c^2 = 3*(-6+b)^2 - b^2 - 2*(9-b)^2 = 

    = 3*(36 - 12b + b^2) - b^2 - 2*(81 - 18b + b^2) = 108 - 36b + 3b^2 - b^2 - 162 + 36b - 2b^2 =

    = combine like terms = -54. 


ANSWER.  If a-b = -6  and  b+c = 9, then the value of 3a%5E2-b%5E2-2c%5E2 is -54.

Solved.