Activity › Discussion › Math › Factorization on cubes in 3 variables › Reply To: Factorization on cubes in 3 variables

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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 righthand 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: