If $a, b, c$ are in A.P., then show that,
$(a + 2 b - c) (2 b + c - a) (c + a - b) = 4 a b c$

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Solution

If $a, b, c$ are in AP then $2 b = a + c$
$\Rightarrow (a + 2 b - c) (2 b + c - a) (c + a - b)$
$\Rightarrow (a + a + c - c) (c + a + c - a) (2 b - b)$
$\Rightarrow (2 a) (2 c) (b)$
$\Rightarrow 4 a b c$

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