Prove that $⎣ ⎡ 1 + a^{2} + a^{4} 1 + a b + a^{2} b^{2} 1 + a c + a^{2} c^{2} 1 + a b + a^{2} b^{2} 1 + b^{2} + b^{4} 1 + b c + b^{2} c^{2} 1 + a c + a^{2} c^{2} 1 + b c + b^{2} c^{2} 1 + c^{2} + c^{2} ⎦ ⎤ = (a - b)^{2} (b - c)^{2} (c - a)^{2}$

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Prove that

⎣ ⎡ 1 + a^{2} + a^{4} 1 + a b + a^{2} b^{2} 1 + a c + a^{2} c^{2} 1 + a b + a^{2} b^{2} 1 + b^{2} + b^{4} 1 + b c + b^{2} c^{2} 1 + a c + a^{2} c^{2} 1 + b c + b^{2} c^{2} 1 + c^{2} + c^{2} ⎦ ⎤ = (a - b)^{2} (b - c)^{2} (c - a)^{2}

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Prove that

⎣ ⎡ 1 + a^{2} + a^{4} 1 + a b + a^{2} b^{2} 1 + a c + a^{2} c^{2} 1 + a b + a^{2} b^{2} 1 + b^{2} + b^{4} 1 + b c + b^{2} c^{2} 1 + a c + a^{2} c^{2} 1 + b c + b^{2} c^{2} 1 + c^{2} + c^{2} ⎦ ⎤ = (a - b)^{2} (b - c)^{2} (c - a)^{2}

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