57.One of the factors of a(b - c) + b(c - a) + c( a - b) is (1) (2a - b) (2) (a + b - c) (3) (a - b - c) (4) (a + b - c)

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∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + a b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3. (b - c) (c - a) (a - b) (a + b + c) (a b + b c + c a)

∣ ∣ ∣ ∣ ∣ \begin{matrix} b c - a^{2} & c a - b^{2} & a b - c^{2} - b c + c a + c b & b c - c a + a b & b c + c a - a b (a + b) (a + c) & (b + c) (b + a) & (c + a) (c + b) \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3 (b - c) (c - a) (a - b) (a + b + c) (b c + c a + a b)

a^{2} (b + c)^{2} + b^{2} (c + a)^{2} + c^{2} (a + b) + a b c (a + b + c) + (a^{2} + b^{2} + c^{2}) (b c + c a + a b)

$2 a b + 3 b c + 4 b a - 2 c b + 3 a b + 8 b c$ equals

a - b + a b, b + c - b c

c - a - a c

2 c + a b - a c - b c

2 c - a b - a c - b c

2 c + a b + a c + b c

2 c - a b + a c + b c

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