What is a(b-c)+b(c-a)+c(a-b) ?

The solution to a(b-c)+b(c-a)+c(a-b) is 0

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simplify a(b-c)+b(c-a)+c(a-b)

simplify

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

0

Solution steps

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

Expand

a (b - c) : ab - a c

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

Expand

b (c - a) : b c - ab

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

Expand

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

= ab - a c + b c - ab + a c - b c

Group like terms

= ab - ab - a c + a c + b c - b c

Add similar elements:

ab - ab = 0

= - a c + a c + b c - b c

Add similar elements:

- a c + a c = 0

= b c - b c

Add similar elements:

b c - b c = 0

= 0

(3 x + y) + (4 x - y) + (7 + y)

\frac{2 i}{i - 3} + \frac{i}{i + 1}

3 (\frac{x + 3}{2 x + 1}) + 2

(5 x^{- 3} y^{0})^{- 1}

\frac{25}{80}