a ,. ,[(b+c) (a+b+c)] is equal to - Vidyadip

MCQ

$a\,.\,[(b+c)\times (a+b+c)]$ is equal to

A
$[a b c]$
B
$2[a b c]$
C
$3[a b c]$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) $a\,.\,[(b + c) \times (a + b + c)]$

$ = a\,.\,(b \times a + b \times b + b \times c) + a\,.\,(c \times a + c \times b + c \times c)$

$ = [a\,b\,a] + [a\,b\,b] + [a{\rm{ }}b{\rm{ }}c] + [a\,c\,a] + [a{\rm{ }}c{\rm{ }}b] + [a{\rm{ }}c{\rm{ }}c]$

$=0 + 0 + [a\,b\,c] + 0 - [a\,b\,c] + 0 = 0.$

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