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Simplifying (x(a + -1) + a)(x(b + -1) + b) = -2x + bx + ax + a + b Reorder the terms: (x(-1 + a) + a)(x(b + -1) + b) = -2x + bx + ax + a + b ((-1 * x + a * x) + a)(x(b + -1) + b) = -2x + bx + ax + a + b Reorder the terms: ((ax + -1x) + a)(x(b + -1) + b) = -2x + bx + ax + a + b ((ax + -1x) + a)(x(b + -1) + b) = -2x + bx + ax + a + b Reorder the terms: (a + ax + -1x)(x(b + -1) + b) = -2x + bx + ax + a + b Reorder the terms: (a + ax + -1x)(x(-1 + b) + b) = -2x + bx + ax + a + b (a + ax + -1x)((-1 * x + b * x) + b) = -2x + bx + ax + a + b Reorder the terms: (a + ax + -1x)((bx + -1x) + b) = -2x + bx + ax + a + b (a + ax + -1x)((bx + -1x) + b) = -2x + bx + ax + a + b Reorder the terms: (a + ax + -1x)(b + bx + -1x) = -2x + bx + ax + a + b Multiply (a + ax + -1x) * (b + bx + -1x) (a(b + bx + -1x) + ax(b + bx + -1x) + -1x * (b + bx + -1x)) = -2x + bx + ax + a + b ((b * a + bx * a + -1x * a) + ax(b + bx + -1x) + -1x * (b + bx + -1x)) = -2x + bx + ax + a + b ((ab + abx + -1ax) + ax(b + bx + -1x) + -1x * (b + bx + -1x)) = -2x + bx + ax + a + b (ab + abx + -1ax + (b * ax + bx * ax + -1x * ax) + -1x * (b + bx + -1x)) = -2x + bx + ax + a + b (ab + abx + -1ax + (abx + abx2 + -1ax2) + -1x * (b + bx + -1x)) = -2x + bx + ax + a + b (ab + abx + -1ax + abx + abx2 + -1ax2 + (b * -1x + bx * -1x + -1x * -1x)) = -2x + bx + ax + a + b (ab + abx + -1ax + abx + abx2 + -1ax2 + (-1bx + -1bx2 + 1x2)) = -2x + bx + ax + a + b Reorder the terms: (ab + abx + abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2) = -2x + bx + ax + a + b Combine like terms: abx + abx = 2abx (ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2) = -2x + bx + ax + a + b Reorder the terms: ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = a + ax + b + bx + -2x Solving ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = a + ax + b + bx + -2x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1a' to each side of the equation. ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + -1a + 1x2 = a + ax + b + bx + -1a + -2x Reorder the terms: -1a + ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = a + ax + b + bx + -1a + -2x Reorder the terms: -1a + ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = a + -1a + ax + b + bx + -2x Combine like terms: a + -1a = 0 -1a + ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = 0 + ax + b + bx + -2x -1a + ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = ax + b + bx + -2x Add '-1ax' to each side of the equation. -1a + ab + 2abx + abx2 + -1ax + -1ax2 + -1bx + -1bx2 + -1ax + 1x2 = ax + b + bx + -1ax + -2x Reorder the terms: -1a + ab + 2abx + abx2 + -1ax + -1ax + -1ax2 + -1bx + -1bx2 + 1x2 = ax + b + bx + -1ax + -2x Combine like terms: -1ax + -1ax = -2ax -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + -1bx2 + 1x2 = ax + b + bx + -1ax + -2x Reorder the terms: -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + -1bx2 + 1x2 = ax + -1ax + b + bx + -2x Combine like terms: ax + -1ax = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + -1bx2 + 1x2 = 0 + b + bx + -2x -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + -1bx2 + 1x2 = b + bx + -2x Add 'bx' to each side of the equation. -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + -1bx2 + bx + 1x2 = b + bx + bx + -2x Reorder the terms: -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx + bx + -1bx2 + 1x2 = b + bx + bx + -2x Combine like terms: -1bx + bx = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + 0 + -1bx2 + 1x2 = b + bx + bx + -2x -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx2 + 1x2 = b + bx + bx + -2x Combine like terms: bx + bx = 2bx -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx2 + 1x2 = b + 2bx + -2x Add 'bx2' to each side of the equation. -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1bx2 + bx2 + 1x2 = b + 2bx + bx2 + -2x Combine like terms: -1bx2 + bx2 = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + 0 + 1x2 = b + 2bx + bx2 + -2x -1a + ab + 2abx + abx2 + -2ax + -1ax2 + 1x2 = b + 2bx + bx2 + -2x Add '-1x2' to each side of the equation. -1a + ab + 2abx + abx2 + -2ax + -1ax2 + 1x2 + -1x2 = b + 2bx + bx2 + -2x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + 0 = b + 2bx + bx2 + -2x + -1x2 -1a + ab + 2abx + abx2 + -2ax + -1ax2 = b + 2bx + bx2 + -2x + -1x2 Reorder the terms: -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = b + -1b + 2bx + -2bx + bx2 + -1bx2 + -2x + 2x + -1x2 + x2 Combine like terms: b + -1b = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 0 + 2bx + -2bx + bx2 + -1bx2 + -2x + 2x + -1x2 + x2 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 2bx + -2bx + bx2 + -1bx2 + -2x + 2x + -1x2 + x2 Combine like terms: 2bx + -2bx = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 0 + bx2 + -1bx2 + -2x + 2x + -1x2 + x2 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = bx2 + -1bx2 + -2x + 2x + -1x2 + x2 Combine like terms: bx2 + -1bx2 = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 0 + -2x + 2x + -1x2 + x2 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 0 + -1x2 + x2 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -1a + ab + 2abx + abx2 + -2ax + -1ax2 + -1b + -2bx + -1bx2 + 2x + x2 = 0 The solution to this equation could not be determined.
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