(a + b) ,. ,(b + c) (a + b + c) = - Vidyadip

MCQ

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

A
$-[a b c]$
✓
$[a b c]$
C
$0$
D
$2[a b c]$

✓

Answer

Correct option: B.

$[a b c]$

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

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

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

$[\because \,\,b \times b = 0\,o\,c \times c = 0]$

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

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

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

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