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

  • Harshwardhan

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    December 15, 2023 at 2:30 pm
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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:

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