Value of the determinant 1 bc a(b+c)1 ca b(c+a)1 ab c(a+b) is

Δ=1 bc ab+bc+ca1 ca ab+bc+ca1 ab ab+bc+caC3↔C3+C2=0 as C1 and C3 are proportional.

Value of the determinant 1 bc a(b+c)1 ca b(c+a)1 ab c(a+b) is

Δ=1 bc ab+bc+ca1 ca ab+bc+ca1 ab ab+bc+caC3↔C3+C2=0 as C1 and C3 are proportional.

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Value of the determinant $|\begin{array}{lll} 1 b c a (b + c) \\ 1 c a b (c + a) \\ 1 a b c (a + b) \end{array}|$ is

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$Δ = |\begin{array}{lll} 1 b c a b + b c + c a \\ 1 c a a b + b c + c a \\ 1 a b a b + b c + c a \end{array}| C_{3} \leftrightarrow C_{3} + C_{2}$

$= 0$ as $C_{1}$ and $C_{3}$ are proportional.

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Value of the determinant 1 bc a(b+c)1 ca b(c+a)1 ab c(a+b) is

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Value of the determinant $|\begin{array}{lll} 1 b c a (b + c) \\ 1 c a b (c + a) \\ 1 a b c (a + b) \end{array}|$ is