SOLUTION: if a+b+c=4, then a�+b�+c�-12c�+48c-64 is equal to (A)3abc-12ab (B)3abc+12ab (C)abc+12ab (D)3abc please show how to solve this question

Question 830735: if a+b+c=4, then
a�+b�+c�-12c�+48c-64 is equal to
(A)3abc-12ab
(B)3abc+12ab
(C)abc+12ab
(D)3abc
please show how to solve this question
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
if a+b+c=4, then
a�+b�+c�-12c�+48c-64 is equal to
(A)3abc-12ab
(B)3abc+12ab
(C)abc+12ab
(D)3abc
please show how to solve this question


          a+b+c = 4
            a+b = 4-c

Cube both sides:

         (a+b)� = (4-c)�
a�+3a�b+3ab�+b� = 64-48c+12c�-c�

We want to find a�+b�+c�-12c�+48c-64,
so we isolate that expression on the left

a�+b�+c�-12c�+48c-64 = -3a�b-3ab� = 

-3ab(b+a) = -3ab(a+b) = -3ab(4-c) = 

-12ab+3abc = 3abc-12ab

So the correct choice is (a). 

Edwin

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