Question
Simplify the following: $a(b - c) + b(c - a) + c(a - b)$
✓
Answer
$a(b - c) + b(c - a) + (a - b)$
$= a \times b - a \times c + b \times c - b \times a + c \times a - c \times b$
$= ab - ac + bc - ab + ac - bc$
$= 0$
$= a \times b - a \times c + b \times c - b \times a + c \times a - c \times b$
$= ab - ac + bc - ab + ac - bc$
$= 0$
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