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Simplifying (1 + -1ax)(1 + -1by)(1 + -1cz) = 0 Multiply (1 + -1ax) * (1 + -1by) (1(1 + -1by) + -1ax * (1 + -1by))(1 + -1cz) = 0 ((1 * 1 + -1by * 1) + -1ax * (1 + -1by))(1 + -1cz) = 0 ((1 + -1by) + -1ax * (1 + -1by))(1 + -1cz) = 0 (1 + -1by + (1 * -1ax + -1by * -1ax))(1 + -1cz) = 0 Reorder the terms: (1 + -1by + (1abxy + -1ax))(1 + -1cz) = 0 (1 + -1by + (1abxy + -1ax))(1 + -1cz) = 0 Reorder the terms: (1 + 1abxy + -1ax + -1by)(1 + -1cz) = 0 (1 + 1abxy + -1ax + -1by)(1 + -1cz) = 0 Multiply (1 + 1abxy + -1ax + -1by) * (1 + -1cz) (1(1 + -1cz) + 1abxy * (1 + -1cz) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 ((1 * 1 + -1cz * 1) + 1abxy * (1 + -1cz) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 ((1 + -1cz) + 1abxy * (1 + -1cz) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 (1 + -1cz + (1 * 1abxy + -1cz * 1abxy) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 Reorder the terms: (1 + -1cz + (-1abcxyz + 1abxy) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 (1 + -1cz + (-1abcxyz + 1abxy) + -1ax * (1 + -1cz) + -1by * (1 + -1cz)) = 0 (1 + -1cz + -1abcxyz + 1abxy + (1 * -1ax + -1cz * -1ax) + -1by * (1 + -1cz)) = 0 Reorder the terms: (1 + -1cz + -1abcxyz + 1abxy + (1acxz + -1ax) + -1by * (1 + -1cz)) = 0 (1 + -1cz + -1abcxyz + 1abxy + (1acxz + -1ax) + -1by * (1 + -1cz)) = 0 (1 + -1cz + -1abcxyz + 1abxy + 1acxz + -1ax + (1 * -1by + -1cz * -1by)) = 0 Reorder the terms: (1 + -1cz + -1abcxyz + 1abxy + 1acxz + -1ax + (1bcyz + -1by)) = 0 (1 + -1cz + -1abcxyz + 1abxy + 1acxz + -1ax + (1bcyz + -1by)) = 0 Reorder the terms: (1 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz) = 0 (1 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz) = 0 Solving 1 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz = 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 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1 + -1cz = 0 + -1 Reorder the terms: 1 + -1 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz = 0 + -1 -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz = 0 + -1 Combine like terms: 0 + -1 = -1 -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1cz = -1 Add '-1bcyz' to each side of the equation. -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1by + -1bcyz + -1cz = -1 + -1bcyz Reorder the terms: -1abcxyz + 1abxy + 1acxz + -1ax + 1bcyz + -1bcyz + -1by + -1cz = -1 + -1bcyz Combine like terms: 1bcyz + -1bcyz = 0 -1abcxyz + 1abxy + 1acxz + -1ax + 0 + -1by + -1cz = -1 + -1bcyz -1abcxyz + 1abxy + 1acxz + -1ax + -1by + -1cz = -1 + -1bcyz Add 'by' to each side of the equation. -1abcxyz + 1abxy + 1acxz + -1ax + -1by + by + -1cz = -1 + -1bcyz + by Combine like terms: -1by + by = 0 -1abcxyz + 1abxy + 1acxz + -1ax + 0 + -1cz = -1 + -1bcyz + by -1abcxyz + 1abxy + 1acxz + -1ax + -1cz = -1 + -1bcyz + by Add 'cz' to each side of the equation. -1abcxyz + 1abxy + 1acxz + -1ax + -1cz + cz = -1 + -1bcyz + by + cz Combine like terms: -1cz + cz = 0 -1abcxyz + 1abxy + 1acxz + -1ax + 0 = -1 + -1bcyz + by + cz -1abcxyz + 1abxy + 1acxz + -1ax = -1 + -1bcyz + by + cz Reorder the terms: 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = -1 + -1bcyz + by + cz + 1 + bcyz + -1by + -1cz Reorder the terms: 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = -1 + 1 + -1bcyz + bcyz + by + -1by + cz + -1cz Combine like terms: -1 + 1 = 0 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = 0 + -1bcyz + bcyz + by + -1by + cz + -1cz 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = -1bcyz + bcyz + by + -1by + cz + -1cz Combine like terms: -1bcyz + bcyz = 0 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = 0 + by + -1by + cz + -1cz 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = by + -1by + cz + -1cz Combine like terms: by + -1by = 0 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = 0 + cz + -1cz 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = cz + -1cz Combine like terms: cz + -1cz = 0 1 + -1abcxyz + 1abxy + 1acxz + -1ax + bcyz + -1by + -1cz = 0 The solution to this equation could not be determined.
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