a×b+a-b+b+c×b-c+c+a×c-a=

(a+b)×(a-b)+(b+c)×(b-c)+(c+a)×(c-a) 0-a×b+b×a-0+0-b×c+c×b-0 0-c×a+a×c-0 =-2(a×b+b×c+c×a)

a×b+a-b+b+c×b-c+c+a×c-a=

(a+b)×(a-b)+(b+c)×(b-c)+(c+a)×(c-a) 0-a×b+b×a-0+0-b×c+c×b-0 0-c×a+a×c-0 =-2(a×b+b×c+c×a)

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

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$- 2 (a \times b + b \times c + c \times a)$

$- (a \times b + b \times c + c \times a)$

$2 (a \times b + b \times c + c \times a)$

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

answer is B.

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Detailed Solution

$\begin{array}{rcl} (a + b) \times (a - b) + (b + c) \times (b - c) + (c + a) \times (c - a) \\ 0 - a \times b + b \times a - 0 + 0 - b \times c + c \times b - 0 \\ 0 - c \times a + a \times c - 0 \\ = & - 2 (a \times b + b \times c + c \times a) \end{array}$