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

Evaluate

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

Rewrite the expression

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

Expand the expression

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

Expand the expression

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

Expand the expression

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

Solution

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

Simplify the expression