If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 38$, then what is the value of $a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2) + 3abc$?

-6

If $a + b + c = 6$

$a^2 + b^2 + c^2 = 38$,

Then what is the value of $a(b^2 + c^2) + b(c^2 + a^2) + c(a^2 + b^2) + 3abc$

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put c = 0

If $a + b  = 6$

$a^2 + b^2 = 38$,

( a + b )² = a² + b² + 2ab

( 6 )² = 38 + 2ab

36 = 38 + 2ab

ab = -1

Then what is the value of $a(b^2) + b(a^2)$ = ab ( a + b)

ab ( a + b) = -1 (6) = -6