If $∣ ∣ a^{2} b^{2} c^{2} (a + 1)^{2} (b + 1)^{2} (c + 1)^{2} (a - 1)^{2} (b - 1)^{2} (c - 1)^{2} ∣ ∣ = k (a - b) (b - c) (c - a),$ then find the value of $k ˙$

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∣ ∣ a^{2} b^{2} c^{2} (a + 1)^{2} (b + 1)^{2} (c + 1)^{2} (a - 1)^{2} (b - 1)^{2} (c - 1)^{2} ∣ ∣ = k (a - b) (b - c) (c - a),

then find the value of

k ˙

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Question Text

∣ ∣ a^{2} b^{2} c^{2} (a + 1)^{2} (b + 1)^{2} (c + 1)^{2} (a - 1)^{2} (b - 1)^{2} (c - 1)^{2} ∣ ∣ = k (a - b) (b - c) (c - a),

then find the value of

k ˙

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