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Simplifying (1 + -1a)(1 + -1b)(1 + -1c) = 0 Multiply (1 + -1a) * (1 + -1b) (1(1 + -1b) + -1a * (1 + -1b))(1 + -1c) = 0 ((1 * 1 + -1b * 1) + -1a * (1 + -1b))(1 + -1c) = 0 ((1 + -1b) + -1a * (1 + -1b))(1 + -1c) = 0 (1 + -1b + (1 * -1a + -1b * -1a))(1 + -1c) = 0 (1 + -1b + (-1a + 1ab))(1 + -1c) = 0 Reorder the terms: (1 + -1a + 1ab + -1b)(1 + -1c) = 0 (1 + -1a + 1ab + -1b)(1 + -1c) = 0 Multiply (1 + -1a + 1ab + -1b) * (1 + -1c) (1(1 + -1c) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = 0 ((1 * 1 + -1c * 1) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = 0 ((1 + -1c) + -1a * (1 + -1c) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = 0 (1 + -1c + (1 * -1a + -1c * -1a) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = 0 (1 + -1c + (-1a + 1ac) + 1ab * (1 + -1c) + -1b * (1 + -1c)) = 0 (1 + -1c + -1a + 1ac + (1 * 1ab + -1c * 1ab) + -1b * (1 + -1c)) = 0 (1 + -1c + -1a + 1ac + (1ab + -1abc) + -1b * (1 + -1c)) = 0 (1 + -1c + -1a + 1ac + 1ab + -1abc + (1 * -1b + -1c * -1b)) = 0 (1 + -1c + -1a + 1ac + 1ab + -1abc + (-1b + 1bc)) = 0 Reorder the terms: (1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c) = 0 (1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c) = 0 Solving 1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1 + -1c = 0 + -1 Reorder the terms: 1 + -1 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = 0 + -1 -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = 0 + -1 Combine like terms: 0 + -1 = -1 -1a + 1ab + -1abc + 1ac + -1b + 1bc + -1c = -1 Add 'b' to each side of the equation. -1a + 1ab + -1abc + 1ac + -1b + 1bc + b + -1c = -1 + b Reorder the terms: -1a + 1ab + -1abc + 1ac + -1b + b + 1bc + -1c = -1 + b Combine like terms: -1b + b = 0 -1a + 1ab + -1abc + 1ac + 0 + 1bc + -1c = -1 + b -1a + 1ab + -1abc + 1ac + 1bc + -1c = -1 + b Add '-1bc' to each side of the equation. -1a + 1ab + -1abc + 1ac + 1bc + -1bc + -1c = -1 + b + -1bc Combine like terms: 1bc + -1bc = 0 -1a + 1ab + -1abc + 1ac + 0 + -1c = -1 + b + -1bc -1a + 1ab + -1abc + 1ac + -1c = -1 + b + -1bc Add 'c' to each side of the equation. -1a + 1ab + -1abc + 1ac + -1c + c = -1 + b + -1bc + c Combine like terms: -1c + c = 0 -1a + 1ab + -1abc + 1ac + 0 = -1 + b + -1bc + c -1a + 1ab + -1abc + 1ac = -1 + b + -1bc + c Reorder the terms: 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = -1 + b + -1bc + c + 1 + -1b + bc + -1c Reorder the terms: 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = -1 + 1 + b + -1b + -1bc + bc + c + -1c Combine like terms: -1 + 1 = 0 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = 0 + b + -1b + -1bc + bc + c + -1c 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = b + -1b + -1bc + bc + c + -1c Combine like terms: b + -1b = 0 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = 0 + -1bc + bc + c + -1c 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = -1bc + bc + c + -1c Combine like terms: -1bc + bc = 0 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = 0 + c + -1c 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = c + -1c Combine like terms: c + -1c = 0 1 + -1a + 1ab + -1abc + 1ac + -1b + bc + -1c = 0 The solution to this equation could not be determined.
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