What is expand (a-1)(b-1)(c-1)(b-a)(c-a)(c-b) ?

The solution to expand (a-1)(b-1)(c-1)(b-a)(c-a)(c-b) is

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expand (a-1)(b-1)(c-1)(b-a)(c-a)(c-b)

expand

(a - 1) (b - 1) (c - 1) (b - a) (c - a) (c - b)

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

Solution steps

(a - 1) (b - 1) (c - 1) (b - a) (c - a) (c - b)

Expand

(a - 1) (b - 1) (c - 1) (b - a) (c - a) (c - b) : (ab - a - b + 1) (c - 1) (b - a) (c - a) (c - b)

= (ab - a - b + 1) (c - 1) (b - a) (c - a) (c - b)

Apply FOIL method

(c - 1) (b - a) : b c - a c - b + a

= (ab - a - b + 1) (b c - a c - b + a) (c - a) (c - b)

Apply FOIL method

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

= (ab - a - b + 1) (b c - a c - b + a) (c^{2} - b c - a c + ab)

Expand

(ab - a - b + 1) (b c - a c - b + a) : - a b^{2} + a^{2} b + a^{2} c - a^{2} + a - b^{2} c + b c - a c + a b^{2} c - a^{2} b c + b^{2} - b

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

Distribute parentheses

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

Simplify

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

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

\frac{2 ( 2 - 3 ) + 10}{4}

(- - y + 1 + 3)^{2}

\frac{4 ( - x ^{2} - 16 )}{( x ^{2} - 16 ) ^{2}}

(1 + i 2)^{4}

(\frac{x}{2} + 3 y) (\frac{x}{4} + 2 y)

What is expand (a-1)(b-1)(c-1)(b-a)(c-a)(c-b) ?
The solution to expand (a-1)(b-1)(c-1)(b-a)(c-a)(c-b) is