Solve a(b-c)3 b(c-a)3 c(a-b)3

Question

Simplify the expression

- 27 a b^{3} c^{2} - 27 a^{3} b^{2} c + 27 a^{2} b^{3} c - 27 a^{2} b c^{3} + 27 a b^{2} c^{3} + 27 a^{3} b c^{2}

Evaluate

a (b - c) \times 3 b (c - a) \times 3 c (a - b) \times 3

Rewrite the expression in exponential form

a (b - c) \times 3^{3} b (c - a) c (a - b)

Multiply the terms

More Steps

27 ab c (b - c) (c - a) (a - b)

Multiply the terms

More Steps

(27 a b^{2} c - 27 ab c^{2}) (c - a) (a - b)

Multiply the terms

More Steps

(27 a b^{2} c^{2} - 27 a^{2} b^{2} c - 27 ab c^{3} + 27 a^{2} b c^{2}) (a - b)

Apply the distributive property

27 a b^{2} c^{2} a - 27 a b^{2} c^{2} b - 27 a^{2} b^{2} c a - (- 27 a^{2} b^{2} c b) - 27 ab c^{3} a - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

27 a^{2} b^{2} c^{2} - 27 a b^{2} c^{2} b - 27 a^{2} b^{2} c a - (- 27 a^{2} b^{2} c b) - 27 ab c^{3} a - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

More Steps

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{2} b^{2} c a - (- 27 a^{2} b^{2} c b) - 27 ab c^{3} a - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

More Steps

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{2} c b) - 27 ab c^{3} a - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

More Steps

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{3} c) - 27 ab c^{3} a - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{3} c) - 27 a^{2} b c^{3} - (- 27 ab c^{3} b) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{3} c) - 27 a^{2} b c^{3} - (- 27 a b^{2} c^{3}) + 27 a^{2} b c^{2} a - 27 a^{2} b c^{2} b

Multiply the terms

More Steps

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{3} c) - 27 a^{2} b c^{3} - (- 27 a b^{2} c^{3}) + 27 a^{3} b c^{2} - 27 a^{2} b c^{2} b

Multiply the terms

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c - (- 27 a^{2} b^{3} c) - 27 a^{2} b c^{3} - (- 27 a b^{2} c^{3}) + 27 a^{3} b c^{2} - 27 a^{2} b^{2} c^{2}

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

27 a^{2} b^{2} c^{2} - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c + 27 a^{2} b^{3} c - 27 a^{2} b c^{3} + 27 a b^{2} c^{3} + 27 a^{3} b c^{2} - 27 a^{2} b^{2} c^{2}

The sum of two opposites equals 0

More Steps

0 - 27 a b^{3} c^{2} - 27 a^{3} b^{2} c + 27 a^{2} b^{3} c - 27 a^{2} b c^{3} + 27 a b^{2} c^{3} + 27 a^{3} b c^{2}

Solution

- 27 a b^{3} c^{2} - 27 a^{3} b^{2} c + 27 a^{2} b^{3} c - 27 a^{2} b c^{3} + 27 a b^{2} c^{3} + 27 a^{3} b c^{2}

Show Solution