Algebra and Applications Test 2

Let x - 1 = a
y - 2 = b
z - 3 = c
Adding these equation, we get:
a + b + c = x - 1 + y - 2 + z - 3
= x + y + z - 6
= 6 - 6 = 0
So, a + b + c = 0
if a + b + c = 0
then ${\mathit{a}}^3+{\mathit{b}}^3+{\mathit{c}}^3=3\mathit{a}\mathit{b}\mathit{c}$
${\left(\mathit{x}-1\right)}^2+{\left(\mathit{y}-2\right)}^2+{\left(\mathit{z}-3\right)}^3$= 3(x - 1) (y - 2)(z - 3)