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