Question

The value of $[( a - b )( b - c )( c - a )]$ is equal to

• A. $1$
• B. $2$
• C. $0$
• D. $2[ a b c ]$

Answer 1

Answer: (C)

$\therefore [(a-b)(b-c)(c-a)]$
$=(a-b) \cdot[(b-c) \times(c-a)] $
$=(a-b) \cdot[b \times c-b \times a-c \times c+c \times a] $
$=(a-b) \cdot[b \times c-b \times a+c \times a]$
$[\because c \times c=0] $
$=a \cdot[b \times c]-a \cdot[b \times a]+a \cdot[c \times a]$
$-b \cdot[b \times c]+b \cdot[b \times a]-b \cdot[c \times a]$
$=[a b c]-0+0+0-[b c a] $
$=[a b c]-[a b c] $
$=0$