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Simplifying (a + b)(b + c)(c + a) = 0 Reorder the terms: (a + b)(b + c)(a + c) = 0 Multiply (a + b) * (b + c) (a(b + c) + b(b + c))(a + c) = 0 ((b * a + c * a) + b(b + c))(a + c) = 0 ((ab + ac) + b(b + c))(a + c) = 0 (ab + ac + (b * b + c * b))(a + c) = 0 Reorder the terms: (ab + ac + (bc + b2))(a + c) = 0 (ab + ac + (bc + b2))(a + c) = 0 (ab + ac + bc + b2)(a + c) = 0 Multiply (ab + ac + bc + b2) * (a + c) (ab(a + c) + ac(a + c) + bc(a + c) + b2(a + c)) = 0 ((a * ab + c * ab) + ac(a + c) + bc(a + c) + b2(a + c)) = 0 Reorder the terms: ((abc + a2b) + ac(a + c) + bc(a + c) + b2(a + c)) = 0 ((abc + a2b) + ac(a + c) + bc(a + c) + b2(a + c)) = 0 (abc + a2b + (a * ac + c * ac) + bc(a + c) + b2(a + c)) = 0 Reorder the terms: (abc + a2b + (ac2 + a2c) + bc(a + c) + b2(a + c)) = 0 (abc + a2b + (ac2 + a2c) + bc(a + c) + b2(a + c)) = 0 (abc + a2b + ac2 + a2c + (a * bc + c * bc) + b2(a + c)) = 0 (abc + a2b + ac2 + a2c + (abc + bc2) + b2(a + c)) = 0 (abc + a2b + ac2 + a2c + abc + bc2 + (a * b2 + c * b2)) = 0 (abc + a2b + ac2 + a2c + abc + bc2 + (ab2 + b2c)) = 0 Reorder the terms: (abc + abc + ab2 + ac2 + a2b + a2c + bc2 + b2c) = 0 Combine like terms: abc + abc = 2abc (2abc + ab2 + ac2 + a2b + a2c + bc2 + b2c) = 0 Solving 2abc + ab2 + ac2 + a2b + a2c + bc2 + b2c = 0 Solving for variable 'a'. The solution to this equation could not be determined.
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