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Simplifying 0 = (a + b + c)(2a + 2b + 2c) Multiply (a + b + c) * (2a + 2b + 2c) 0 = (a(2a + 2b + 2c) + b(2a + 2b + 2c) + c(2a + 2b + 2c)) 0 = ((2a * a + 2b * a + 2c * a) + b(2a + 2b + 2c) + c(2a + 2b + 2c)) Reorder the terms: 0 = ((2ab + 2ac + 2a2) + b(2a + 2b + 2c) + c(2a + 2b + 2c)) 0 = ((2ab + 2ac + 2a2) + b(2a + 2b + 2c) + c(2a + 2b + 2c)) 0 = (2ab + 2ac + 2a2 + (2a * b + 2b * b + 2c * b) + c(2a + 2b + 2c)) Reorder the terms: 0 = (2ab + 2ac + 2a2 + (2ab + 2bc + 2b2) + c(2a + 2b + 2c)) 0 = (2ab + 2ac + 2a2 + (2ab + 2bc + 2b2) + c(2a + 2b + 2c)) 0 = (2ab + 2ac + 2a2 + 2ab + 2bc + 2b2 + (2a * c + 2b * c + 2c * c)) 0 = (2ab + 2ac + 2a2 + 2ab + 2bc + 2b2 + (2ac + 2bc + 2c2)) Reorder the terms: 0 = (2ab + 2ab + 2ac + 2ac + 2a2 + 2bc + 2bc + 2b2 + 2c2) Combine like terms: 2ab + 2ab = 4ab 0 = (4ab + 2ac + 2ac + 2a2 + 2bc + 2bc + 2b2 + 2c2) Combine like terms: 2ac + 2ac = 4ac 0 = (4ab + 4ac + 2a2 + 2bc + 2bc + 2b2 + 2c2) Combine like terms: 2bc + 2bc = 4bc 0 = (4ab + 4ac + 2a2 + 4bc + 2b2 + 2c2) Solving 0 = 4ab + 4ac + 2a2 + 4bc + 2b2 + 2c2 Solving for variable 'a'. Remove the zero: -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 4ab + 4ac + 2a2 + 4bc + 2b2 + 2c2 + -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 Reorder the terms: -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 4ab + -4ab + 4ac + -4ac + 2a2 + -2a2 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 Combine like terms: 4ab + -4ab = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 + 4ac + -4ac + 2a2 + -2a2 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 4ac + -4ac + 2a2 + -2a2 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 Combine like terms: 4ac + -4ac = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 + 2a2 + -2a2 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 2a2 + -2a2 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 Combine like terms: 2a2 + -2a2 = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 + 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 4bc + -4bc + 2b2 + -2b2 + 2c2 + -2c2 Combine like terms: 4bc + -4bc = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 + 2b2 + -2b2 + 2c2 + -2c2 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 2b2 + -2b2 + 2c2 + -2c2 Combine like terms: 2b2 + -2b2 = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 + 2c2 + -2c2 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 2c2 + -2c2 Combine like terms: 2c2 + -2c2 = 0 -4ab + -4ac + -2a2 + -4bc + -2b2 + -2c2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(2ab + 2ac + a2 + 2bc + b2 + c2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(2ab + 2ac + a2 + 2bc + b2 + c2)' equal to zero and attempt to solve: Simplifying 2ab + 2ac + a2 + 2bc + b2 + c2 = 0 Solving 2ab + 2ac + a2 + 2bc + b2 + c2 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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