(a + b)·a1 + (b + c)·b1 + (c + a)·c1=

=(a+b)·b×c[a b c]+(b+c)·c×a[a b c]+(c +a)·a×b[a b c] =1+0+1+0+1+0=3

(a + b)·a1 + (b + c)·b1 + (c + a)·c1=

=(a+b)·b×c[a b c]+(b+c)·c×a[a b c]+(c +a)·a×b[a b c] =1+0+1+0+1+0=3

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$(a + b) \cdot a^{1} + (b + c) \cdot b^{1} + (c + a) \cdot c^{1} =$

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Detailed Solution

$\begin{array}{rcl} = & (a + b) \cdot (\frac{b \times c}{[a b c]}) + (b + c) \cdot (\frac{c \times a}{[a b c]}) + (c + a) \cdot (\frac{a \times b}{[a b c]}) \\ = & 1 + 0 + 1 + 0 + 1 + 0 = 3 \end{array}$

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