What is the Formula of X^3+y^3+z^3-3xyz?

The formula of X^3+y^3+z^3-3xyz is (x+y+z)(x²+y²+z²−xy−yz−zx).

Proof of x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−zx)

x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−zx)

Assume L.H.S=x³+y³+z³−3xyz and R.H.S=(x+y+z)(x²+y²+z²−xy−yz−zx)

First take R.H.S

(x+y+z)(x²+y²+z²−xy−yz−zx)

To multiply two polynomials, we multiply each monomial of one polynomial (with its sign) by each monomial (with its sign) of the other polynomial.

x.x²+x.y²+x.z²−x²y−xyz−x²z+y.x²+y.y²+y.z²−xy²−y²z−xyz+z.x²+z.y²+z.z²−xyz−yz²−xz²

= x³+xy²+xz²−x²y−x²y+yx²+y³−xy²−y²z+x²z+y²z+z³−yz²−xz²−3xyz

= x³+y³+z³−3xyz

L.H.S = R.H.S

x³+y³+z³−3xyz=x³+y³+z³−3xyz

Therefore, x³+y³+z³−3xyz=(x+y+z)(x²+y²+z²−xy−yz−zx).

What is x^3+y^3+z^3-3xyz Factorization?

The factorization of the expression x^3+y^3+z^3−3xyz is (x+y+z)(x^2+y^2+z^2-xy-yz-zx)

What is x cube + y cube + z cube minus 3 x y z Formula?

The x cube + y cube + z cube minus 3 x y z Formula is (x + y+z) (x square + y square + z square – xy – yz – zx).

x3+y3+z3-3xyz=1/2(x+y+z) (x-y)2+(y-z)2+(z-x)2

The equation x^3 + y^3 + z^3 – 3xyz = 1/2(x + y + z) [(x – y)^2 + (y – z)^2 + (z – x)^2] is indeed true.