Solve (a-b)(b-c) (b - c)(a - c) (a - c)(a - b)

Question

Simplify the expression

a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} + 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 2 a^{2} b^{3} c + 2 a b^{3} c^{2} + 2 a b^{2} c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c^{3} + b^{2} c^{4}

Evaluate

(a - b) (b - c) (b - c) (a - c) (a - c) (a - b)

Multiply the first two terms

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

Multiply the first two terms

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

Multiply the terms

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

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

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

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

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

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

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

Multiply the terms

More Steps

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

Apply the distributive property

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

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

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c \times c^{2} - 2 ab c^{2} a^{2} - (- 2 ab c^{2} \times 2 a c) - 2 ab c^{2} \times c^{2} + b^{4} a^{2} - b^{4} \times 2 a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 ab c^{2} a^{2} - (- 2 ab c^{2} \times 2 a c) - 2 ab c^{2} \times c^{2} + b^{4} a^{2} - b^{4} \times 2 a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 2 ab c^{2} \times 2 a c) - 2 ab c^{2} \times c^{2} + b^{4} a^{2} - b^{4} \times 2 a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{2} \times c^{2} + b^{4} a^{2} - b^{4} \times 2 a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - b^{4} \times 2 a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Use the commutative property to reorder the terms

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 2 b^{3} c \times 2 a c) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 4 b^{3} c^{2} a) - 2 b^{3} c \times c^{2} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 4 b^{3} c^{2} a) - 2 b^{3} c^{3} + b^{2} c^{2} a^{2} - b^{2} c^{2} \times 2 a c + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 4 b^{3} c^{2} a) - 2 b^{3} c^{3} + b^{2} c^{2} a^{2} - 2 b^{2} c^{3} a + b^{2} c^{2} \times c^{2}

Multiply the terms

More Steps

a^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c - (- 4 a^{3} b c^{2}) - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} - (- 4 a^{2} b^{3} c) - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} - (- 4 a^{2} b c^{3}) - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} - (- 4 b^{3} c^{2} a) - 2 b^{3} c^{3} + b^{2} c^{2} a^{2} - 2 b^{2} c^{3} a + b^{2} c^{4}

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^{4} b^{2} - 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c + 4 a^{3} b c^{2} - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 4 a^{2} b^{3} c - 2 a b^{3} c^{2} + 4 a^{3} b^{2} c - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} + 4 a^{2} b c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} + b^{2} c^{2} a^{2} - 2 b^{2} c^{3} a + b^{2} c^{4}

Add the terms

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a^{4} b^{2} + 2 a^{3} b^{2} c + a^{2} b^{2} c^{2} - 2 a^{4} b c + 4 a^{3} b c^{2} - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 4 a^{2} b^{3} c - 2 a b^{3} c^{2} - 8 a^{2} b^{2} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} + 4 a^{2} b c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} + b^{2} c^{2} a^{2} - 2 b^{2} c^{3} a + b^{2} c^{4}

Calculate the sum or difference

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 4 a^{3} b c^{2} - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 4 a^{2} b^{3} c - 2 a b^{3} c^{2} + 4 a b^{2} c^{3} - 2 a^{3} b c^{2} + 4 a^{2} b c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} - 2 b^{2} c^{3} a + b^{2} c^{4}

Subtract the terms

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} - 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 4 a^{2} b^{3} c - 2 a b^{3} c^{2} + 4 a b^{2} c^{3} + 4 a^{2} b c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} - 2 b^{2} c^{3} a + b^{2} c^{4}

Add the terms

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} + 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 4 a^{2} b^{3} c - 2 a b^{3} c^{2} + 4 a b^{2} c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c a^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} - 2 b^{2} c^{3} a + b^{2} c^{4}

Subtract the terms

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} + 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 2 a^{2} b^{3} c - 2 a b^{3} c^{2} + 4 a b^{2} c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} + 4 b^{3} c^{2} a - 2 b^{3} c^{3} - 2 b^{2} c^{3} a + b^{2} c^{4}

Add the terms

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} + 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 2 a^{2} b^{3} c + 2 a b^{3} c^{2} + 4 a b^{2} c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c^{3} - 2 b^{2} c^{3} a + b^{2} c^{4}

Solution

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a^{4} b^{2} + 2 a^{3} b^{2} c - 6 a^{2} b^{2} c^{2} - 2 a^{4} b c + 2 a^{3} b c^{2} + 2 a^{2} b c^{3} + a^{4} c^{2} - 2 a^{3} c^{3} + a^{2} c^{4} - 2 a^{3} b^{3} + 2 a^{2} b^{3} c + 2 a b^{3} c^{2} + 2 a b^{2} c^{3} - 2 ab c^{4} + b^{4} a^{2} - 2 b^{4} a c + b^{4} c^{2} - 2 b^{3} c^{3} + b^{2} c^{4}

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