If a, ,b, ,c are in A.P., then (a + 2b - c) (2b + c - a) (c + a -… - Vidyadip

MCQ

If $a,\,b,\,c$ are in $A.P.$, then $(a + 2b - c)$ $(2b + c - a)$ $(c + a - b)$ equals

A
$\frac{1}{2}abc$
B
$abc$
C
$2\ abc$
✓
$4\ abc$

✓

Answer

Correct option: D.

$4\ abc$

d
(d) $(a + 2b - c)\,(2b + c - a)\,(c + a - b)$

$ = (a + a + c - c)(a + c + c - a)(2b - b)$ $ = 4\,abc.$

$(\because a,b,c$ are in $A.P.$,

$\therefore 2b = a + c)$.

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