Question 1209407
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If a+c=-8 and c-b=-4, find the value of {{{3a^2-6b^20+3c^2}}}.
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      My interior voice tells me that the correct problem is THIS


                If   a + c = -8   and   c - b = -4,   find the value of   {{{3a^2-6b^2+3c^2}}}.         (*)


        I will solve in this formulation



<pre>
We have 

    a + c = -8,    (1)

    c - b = -4.    (2)



Subtract eq(2) from eq(1).  You will get

    a + b = -4     (3)


Now 

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


            here replace  (a+b)  by -4 based on (3);  replace  (b-c) by 4  based on (2),  and continue


    = 3*((a-b)*(-4) - 4*(b+c)) = 3*4(b-a)-(b+c)) = 12*(-a-c) = 


            here replace (-a-c)  by 8,  based on (1),  and continue


    = 12*8 = 96.


<U>ANSWER</U>.  After simplifications, the value of  (*)  is  96.
</pre>

Solved.