What is (1)(y-z)^3+(z-x)^3+(x-y)^3 ?

The solution to (1)(y-z)^3+(z-x)^3+(x-y)^3 is -3y^2z+3yz^2-3z^2x+3zx^2-3yx^2+3y^2x

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simplify (1)(y-z)^3+(z-x)^3+(x-y)^3

simplify

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

- 3 y^{2} z + 3 y z^{2} - 3 z^{2} x + 3 z x^{2} - 3 y x^{2} + 3 y^{2} x

Solution steps

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

Simplify

(1) (y - z)^{3} : (y - z)^{3}

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

Expand

(y - z)^{3} : y^{3} - 3 y^{2} z + 3 y z^{2} - z^{3}

= y^{3} - 3 y^{2} z + 3 y z^{2} - z^{3} + (z - x)^{3} + (x - y)^{3}

Expand

(z - x)^{3} : z^{3} - 3 z^{2} x + 3 z x^{2} - x^{3}

= y^{3} - 3 y^{2} z + 3 y z^{2} - z^{3} + z^{3} - 3 z^{2} x + 3 z x^{2} - x^{3} + (x - y)^{3}

Expand

(x - y)^{3} : x^{3} - 3 y x^{2} + 3 y^{2} x - y^{3}

= y^{3} - 3 y^{2} z + 3 y z^{2} - z^{3} + z^{3} - 3 z^{2} x + 3 z x^{2} - x^{3} + x^{3} - 3 y x^{2} + 3 y^{2} x - y^{3}

Add similar elements:

- z^{3} + z^{3} = 0

= y^{3} - 3 y^{2} z + 3 y z^{2} - 3 z^{2} x + 3 z x^{2} - x^{3} + x^{3} - 3 y x^{2} + 3 y^{2} x - y^{3}

Add similar elements:

- x^{3} + x^{3} = 0

= y^{3} - 3 y^{2} z + 3 y z^{2} - 3 z^{2} x + 3 z x^{2} - 3 y x^{2} + 3 y^{2} x - y^{3}

Group like terms

= y^{3} - y^{3} - 3 y^{2} z + 3 y z^{2} - 3 z^{2} x + 3 z x^{2} - 3 y x^{2} + 3 y^{2} x

Add similar elements:

y^{3} - y^{3} = 0

= - 3 y^{2} z + 3 y z^{2} - 3 z^{2} x + 3 z x^{2} - 3 y x^{2} + 3 y^{2} x

125 + 375 - 568 + 768 + a - a

(- 4 x - 10)^{3}

\frac{m}{m} + 1 + \frac{1}{m} + 1 + \frac{1}{m ^{2}} - 1

9 x^{2} - \frac{y ^{2}}{100}

9 m^{2} - 4 n^{2}

What is (1)(y-z)^3+(z-x)^3+(x-y)^3 ?
The solution to (1)(y-z)^3+(z-x)^3+(x-y)^3 is -3y^2z+3yz^2-3z^2x+3zx^2-3yx^2+3y^2x