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Simplifying abx = (a + b + x)(bx + ax + ab) Reorder the terms: abx = (a + b + x)(ab + ax + bx) Multiply (a + b + x) * (ab + ax + bx) abx = (a(ab + ax + bx) + b(ab + ax + bx) + x(ab + ax + bx)) abx = ((ab * a + ax * a + bx * a) + b(ab + ax + bx) + x(ab + ax + bx)) Reorder the terms: abx = ((abx + a2b + a2x) + b(ab + ax + bx) + x(ab + ax + bx)) abx = ((abx + a2b + a2x) + b(ab + ax + bx) + x(ab + ax + bx)) abx = (abx + a2b + a2x + (ab * b + ax * b + bx * b) + x(ab + ax + bx)) Reorder the terms: abx = (abx + a2b + a2x + (abx + ab2 + b2x) + x(ab + ax + bx)) abx = (abx + a2b + a2x + (abx + ab2 + b2x) + x(ab + ax + bx)) abx = (abx + a2b + a2x + abx + ab2 + b2x + (ab * x + ax * x + bx * x)) abx = (abx + a2b + a2x + abx + ab2 + b2x + (abx + ax2 + bx2)) Reorder the terms: abx = (abx + abx + abx + ab2 + ax2 + a2b + a2x + bx2 + b2x) Combine like terms: abx + abx = 2abx abx = (2abx + abx + ab2 + ax2 + a2b + a2x + bx2 + b2x) Combine like terms: 2abx + abx = 3abx abx = (3abx + ab2 + ax2 + a2b + a2x + bx2 + b2x) Solving abx = 3abx + ab2 + ax2 + a2b + a2x + bx2 + b2x Solving for variable 'a'. Combine like terms: abx + -3abx = -2abx -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 3abx + ab2 + ax2 + a2b + a2x + bx2 + b2x + -3abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x Reorder the terms: -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 3abx + -3abx + ab2 + -1ab2 + ax2 + -1ax2 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x Combine like terms: 3abx + -3abx = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + ab2 + -1ab2 + ax2 + -1ax2 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = ab2 + -1ab2 + ax2 + -1ax2 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x Combine like terms: ab2 + -1ab2 = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + ax2 + -1ax2 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = ax2 + -1ax2 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x Combine like terms: ax2 + -1ax2 = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = a2b + -1a2b + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x Combine like terms: a2b + -1a2b = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = a2x + -1a2x + bx2 + -1bx2 + b2x + -1b2x Combine like terms: a2x + -1a2x = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + bx2 + -1bx2 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = bx2 + -1bx2 + b2x + -1b2x Combine like terms: bx2 + -1bx2 = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 + b2x + -1b2x -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = b2x + -1b2x Combine like terms: b2x + -1b2x = 0 -2abx + -1ab2 + -1ax2 + -1a2b + -1a2x + -1bx2 + -1b2x = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2abx + ab2 + ax2 + a2b + a2x + bx2 + b2x) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2abx + ab2 + ax2 + a2b + a2x + bx2 + b2x)' equal to zero and attempt to solve: Simplifying 2abx + ab2 + ax2 + a2b + a2x + bx2 + b2x = 0 Solving 2abx + ab2 + ax2 + a2b + a2x + bx2 + b2x = 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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