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

Question

Simplify the expression

- a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} + a^{4} b^{2} c^{3}

Evaluate

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

Multiply the terms

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

Multiply the terms

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

Multiply the terms

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(a^{2} b^{3} c^{3} - a^{3} b^{3} c^{2} - a^{2} b^{2} c^{4} + a^{3} b^{2} c^{3}) (a - b)

Apply the distributive property

a^{2} b^{3} c^{3} a - a^{2} b^{3} c^{3} b - a^{3} b^{3} c^{2} a - (- a^{3} b^{3} c^{2} b) - a^{2} b^{2} c^{4} a - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{3} c^{3} b - a^{3} b^{3} c^{2} a - (- a^{3} b^{3} c^{2} b) - a^{2} b^{2} c^{4} a - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{3} b^{3} c^{2} a - (- a^{3} b^{3} c^{2} b) - a^{2} b^{2} c^{4} a - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{3} c^{2} b) - a^{2} b^{2} c^{4} a - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{4} c^{2}) - a^{2} b^{2} c^{4} a - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{4} c^{2}) - a^{3} b^{2} c^{4} - (- a^{2} b^{2} c^{4} b) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{4} c^{2}) - a^{3} b^{2} c^{4} - (- a^{2} b^{3} c^{4}) + a^{3} b^{2} c^{3} a - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{4} c^{2}) - a^{3} b^{2} c^{4} - (- a^{2} b^{3} c^{4}) + a^{4} b^{2} c^{3} - a^{3} b^{2} c^{3} b

Multiply the terms

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a^{3} b^{3} c^{3} - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} - (- a^{3} b^{4} c^{2}) - a^{3} b^{2} c^{4} - (- a^{2} b^{3} c^{4}) + a^{4} b^{2} 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^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} + a^{4} b^{2} c^{3} - a^{3} b^{3} c^{3}

The sum of two opposites equals 0

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0 - a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} + a^{4} b^{2} c^{3}

Solution

- a^{2} b^{4} c^{3} - a^{4} b^{3} c^{2} + a^{3} b^{4} c^{2} - a^{3} b^{2} c^{4} + a^{2} b^{3} c^{4} + a^{4} b^{2} c^{3}

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