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Simplifying (a + b + c)(a + -1b + -1c) = a2 + -1b2 + 2bc + -1c2 Multiply (a + b + c) * (a + -1b + -1c) (a(a + -1b + -1c) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 ((a * a + -1b * a + -1c * a) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 Reorder the terms: ((-1ab + -1ac + a2) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 ((-1ab + -1ac + a2) + b(a + -1b + -1c) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 (-1ab + -1ac + a2 + (a * b + -1b * b + -1c * b) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 Reorder the terms: (-1ab + -1ac + a2 + (ab + -1bc + -1b2) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 (-1ab + -1ac + a2 + (ab + -1bc + -1b2) + c(a + -1b + -1c)) = a2 + -1b2 + 2bc + -1c2 (-1ab + -1ac + a2 + ab + -1bc + -1b2 + (a * c + -1b * c + -1c * c)) = a2 + -1b2 + 2bc + -1c2 (-1ab + -1ac + a2 + ab + -1bc + -1b2 + (ac + -1bc + -1c2)) = a2 + -1b2 + 2bc + -1c2 Reorder the terms: (-1ab + ab + -1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 Combine like terms: -1ab + ab = 0 (0 + -1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 (-1ac + ac + a2 + -1bc + -1bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 Combine like terms: -1ac + ac = 0 (0 + a2 + -1bc + -1bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 (a2 + -1bc + -1bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 Combine like terms: -1bc + -1bc = -2bc (a2 + -2bc + -1b2 + -1c2) = a2 + -1b2 + 2bc + -1c2 Reorder the terms: a2 + -2bc + -1b2 + -1c2 = a2 + 2bc + -1b2 + -1c2 Add '-1a2' to each side of the equation. a2 + -2bc + -1b2 + -1a2 + -1c2 = a2 + 2bc + -1b2 + -1a2 + -1c2 Reorder the terms: a2 + -1a2 + -2bc + -1b2 + -1c2 = a2 + 2bc + -1b2 + -1a2 + -1c2 Combine like terms: a2 + -1a2 = 0 0 + -2bc + -1b2 + -1c2 = a2 + 2bc + -1b2 + -1a2 + -1c2 -2bc + -1b2 + -1c2 = a2 + 2bc + -1b2 + -1a2 + -1c2 Reorder the terms: -2bc + -1b2 + -1c2 = a2 + -1a2 + 2bc + -1b2 + -1c2 Combine like terms: a2 + -1a2 = 0 -2bc + -1b2 + -1c2 = 0 + 2bc + -1b2 + -1c2 -2bc + -1b2 + -1c2 = 2bc + -1b2 + -1c2 Add 'b2' to each side of the equation. -2bc + -1b2 + b2 + -1c2 = 2bc + -1b2 + b2 + -1c2 Combine like terms: -1b2 + b2 = 0 -2bc + 0 + -1c2 = 2bc + -1b2 + b2 + -1c2 -2bc + -1c2 = 2bc + -1b2 + b2 + -1c2 Combine like terms: -1b2 + b2 = 0 -2bc + -1c2 = 2bc + 0 + -1c2 -2bc + -1c2 = 2bc + -1c2 Add 'c2' to each side of the equation. -2bc + -1c2 + c2 = 2bc + -1c2 + c2 Combine like terms: -1c2 + c2 = 0 -2bc + 0 = 2bc + -1c2 + c2 -2bc = 2bc + -1c2 + c2 Combine like terms: -1c2 + c2 = 0 -2bc = 2bc + 0 -2bc = 2bc Solving -2bc = 2bc Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-2bc' to each side of the equation. -2bc + -2bc = 2bc + -2bc Combine like terms: -2bc + -2bc = -4bc -4bc = 2bc + -2bc Combine like terms: 2bc + -2bc = 0 -4bc = 0 Divide each side by '-4'. bc = 0 Simplifying bc = 0 The solution to this equation could not be determined.
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