Naming Numbers Worksheets for Grade 1 
Tracing Letter Writing Foundational Worksheet -
Factorization on cubes in 3 variables
What is x^3+y^3+z^3 equal to if x+y+z = 0
Prove that x^3+y^3+z^3 – 3xyz = (x+y+z)(x^2+y^2+z^2-xy-yz-zx)
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The equation in the image is:
We are also given that:
We can use the given equation to solve for the value of c3 + y3 + z3.
One way to solve for + y3 + z3 is to use the factorization:
3 (c + y + -f- -F z2 — cy — zz — yz)
We can see that the first term on the right-hand side of this equation is equal to O, since we are given that c + y +z O. Therefore, we have:
-F y3 -F z3 = O = (c -F y -F -F Y2 -F z2 — cy — cz — yz)
This means that either c + y + z = O or c2 + Y2 + z2 — cy — cz — yz O.
If c + y + z = O, then we have already shown that c3 + y3 + z3 O.
If æ2 + Y2 + z2 — cy — cz — yz 0, then we can rearrange this equation to get:
