Algebra and Applications Test 1

Let a - 4 = x
b - 3 = y
c - 1 = z
Adding these equations we get:
x + y + z = a - 4 + b - 3 + c - 1
= a + b + c - 8
= 8 - 8 = 0
= x + y + z = 0
We have an identity
if x + y + z = 0
then ${\mathit{x}}^3+{\mathit{y}}^3+{\mathit{z}}^3-3\mathit{x}\mathit{y}\mathit{z}=0$
${\left(\mathit{a}-4\right)}^3+{\left(\mathit{b}-3\right)}^3+{\left(\mathit{c}-1\right)}^3$ $-3\left(\mathit{a}-4\right)\left(\mathit{b}-3\right)\left(\mathit{c}-1\right)=0$