Question

What is the formula of x+y+z whole cube is it = x cube + y cube + z cube - 3xyz

Answer 1

Answer:

$(x + y + z) {}^{3} = x {}^{3} + y {}^{3} + z {}^{3} + 3(x + y)(y + z)(x + z)$

Answer 2

We must recall that:

If $x+y+z=0$

⇒ $x+y=-z$

Cubing both sides

⇒ $x^3+y^3+3x^2y+3xy^2=-z^3$

⇒ $x^3+y^3+3xy(x+y)=-z^3$

⇒ $x^3+y^3+3xy(-z)=-z^3$

⇒ $x^3+y^3+z^3-3xyz=0$