Solve (x - y)3 (y - z)3 (z - x)3

Evaluate

(x - y) \times 3 (y - z) \times 3 (z - x) \times 3

Rewrite the expression in exponential form

(x - y) \times 3^{3} (y - z) (z - x)

Multiply the first two terms

3^{3} (x - y) (y - z) (z - x)

Evaluate the power

27 (x - y) (y - z) (z - x)

Multiply the terms

(27 x - 27 y) (y - z) (z - x)

Multiply the terms

More Steps

(27 x y - 27 x z - 27 y^{2} + 27 yz) (z - x)

Apply the distributive property

27 x yz - 27 x y x - 27 x z \times z - (- 27 x z x) - 27 y^{2} z - (- 27 y^{2} x) + 27 yz \times z - 27 yz x

Multiply the terms

27 x yz - 27 x^{2} y - 27 x z \times z - (- 27 x z x) - 27 y^{2} z - (- 27 y^{2} x) + 27 yz \times z - 27 yz x

Multiply the terms

27 x yz - 27 x^{2} y - 27 x z^{2} - (- 27 x z x) - 27 y^{2} z - (- 27 y^{2} x) + 27 yz \times z - 27 yz x

Multiply the terms

27 x yz - 27 x^{2} y - 27 x z^{2} - (- 27 x^{2} z) - 27 y^{2} z - (- 27 y^{2} x) + 27 yz \times z - 27 yz x

Multiply the terms

27 x yz - 27 x^{2} y - 27 x z^{2} - (- 27 x^{2} z) - 27 y^{2} z - (- 27 y^{2} x) + 27 y z^{2} - 27 yz x

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

27 x yz - 27 x^{2} y - 27 x z^{2} + 27 x^{2} z - 27 y^{2} z + 27 y^{2} x + 27 y z^{2} - 27 yz x

Subtract the terms

More Steps

0 - 27 x^{2} y - 27 x z^{2} + 27 x^{2} z - 27 y^{2} z + 27 y^{2} x + 27 y z^{2}

Solution

- 27 x^{2} y - 27 x z^{2} + 27 x^{2} z - 27 y^{2} z + 27 y^{2} x + 27 y z^{2}

Simplify the expression