Solve a(b^2-c^2) b(c^2-a^2) c(a^2-b^2)

Question

a (b^{2} - c^{2}) b (c^{2} - a^{2}) c (a^{2} - b^{2})

Simplify the expression

- a b^{5} c^{3} - a^{5} b^{3} c + a^{3} b^{5} c - a^{3} b c^{5} + a b^{3} c^{5} + a^{5} b c^{3}

Evaluate

a (b^{2} - c^{2}) b (c^{2} - a^{2}) c (a^{2} - b^{2})

Multiply the terms

ab c (b^{2} - c^{2}) (c^{2} - a^{2}) (a^{2} - b^{2})

Multiply the terms

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(a b^{3} c - ab c^{3}) (c^{2} - a^{2}) (a^{2} - b^{2})

Multiply the terms

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(a b^{3} c^{3} - a^{3} b^{3} c - ab c^{5} + a^{3} b c^{3}) (a^{2} - b^{2})

Apply the distributive property

a b^{3} c^{3} a^{2} - a b^{3} c^{3} b^{2} - a^{3} b^{3} c a^{2} - (- a^{3} b^{3} c b^{2}) - ab c^{5} a^{2} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{3} c^{3} b^{2} - a^{3} b^{3} c a^{2} - (- a^{3} b^{3} c b^{2}) - ab c^{5} a^{2} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{3} b^{3} c a^{2} - (- a^{3} b^{3} c b^{2}) - ab c^{5} a^{2} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{3} c b^{2}) - ab c^{5} a^{2} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{5} c) - ab c^{5} a^{2} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{5} c) - a^{3} b c^{5} - (- ab c^{5} b^{2}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{5} c) - a^{3} b c^{5} - (- a b^{3} c^{5}) + a^{3} b c^{3} a^{2} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{5} c) - a^{3} b c^{5} - (- a b^{3} c^{5}) + a^{5} b c^{3} - a^{3} b c^{3} b^{2}

Multiply the terms

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a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c - (- a^{3} b^{5} c) - a^{3} b c^{5} - (- a b^{3} c^{5}) + a^{5} b c^{3} - a^{3} b^{3} c^{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

a^{3} b^{3} c^{3} - a b^{5} c^{3} - a^{5} b^{3} c + a^{3} b^{5} c - a^{3} b c^{5} + a b^{3} c^{5} + a^{5} b c^{3} - a^{3} b^{3} c^{3}

The sum of two opposites equals 0

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0 - a b^{5} c^{3} - a^{5} b^{3} c + a^{3} b^{5} c - a^{3} b c^{5} + a b^{3} c^{5} + a^{5} b c^{3}

Solution

- a b^{5} c^{3} - a^{5} b^{3} c + a^{3} b^{5} c - a^{3} b c^{5} + a b^{3} c^{5} + a^{5} b c^{3}

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Factor the expression

ab c (b + c) (b - c) (c + a) (c - a) (a + b) (a - b)

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