Solve x(y^2-z^2) y(z^2-x^2) z(x^2-y^2)

Question

Simplify the expression

- x y^{5} z^{3} - x^{5} y^{3} z + x^{3} y^{5} z - x^{3} y z^{5} + x y^{3} z^{5} + x^{5} y z^{3}

Evaluate

x (y^{2} - z^{2}) y (z^{2} - x^{2}) z (x^{2} - y^{2})

Multiply the terms

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

Multiply the terms

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

Multiply the terms

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(x y^{3} z^{3} - x^{3} y^{3} z - x y z^{5} + x^{3} y z^{3}) (x^{2} - y^{2})

Apply the distributive property

x y^{3} z^{3} x^{2} - x y^{3} z^{3} y^{2} - x^{3} y^{3} z x^{2} - (- x^{3} y^{3} z y^{2}) - x y z^{5} x^{2} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{3} z^{3} y^{2} - x^{3} y^{3} z x^{2} - (- x^{3} y^{3} z y^{2}) - x y z^{5} x^{2} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{3} y^{3} z x^{2} - (- x^{3} y^{3} z y^{2}) - x y z^{5} x^{2} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{3} z y^{2}) - x y z^{5} x^{2} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{5} z) - x y z^{5} x^{2} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{5} z) - x^{3} y z^{5} - (- x y z^{5} y^{2}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{5} z) - x^{3} y z^{5} - (- x y^{3} z^{5}) + x^{3} y z^{3} x^{2} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{5} z) - x^{3} y z^{5} - (- x y^{3} z^{5}) + x^{5} y z^{3} - x^{3} y z^{3} y^{2}

Multiply the terms

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x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z - (- x^{3} y^{5} z) - x^{3} y z^{5} - (- x y^{3} z^{5}) + x^{5} y z^{3} - x^{3} y^{3} z^{3}

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

x^{3} y^{3} z^{3} - x y^{5} z^{3} - x^{5} y^{3} z + x^{3} y^{5} z - x^{3} y z^{5} + x y^{3} z^{5} + x^{5} y z^{3} - x^{3} y^{3} z^{3}

The sum of two opposites equals 0

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0 - x y^{5} z^{3} - x^{5} y^{3} z + x^{3} y^{5} z - x^{3} y z^{5} + x y^{3} z^{5} + x^{5} y z^{3}

Solution

- x y^{5} z^{3} - x^{5} y^{3} z + x^{3} y^{5} z - x^{3} y z^{5} + x y^{3} z^{5} + x^{5} y z^{3}

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Factor the expression

x yz (y + z) (y - z) (z + x) (z - x) (x + y) (x - y)

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