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Simplifying (x + -1y)(x + y) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 Multiply (x + -1y) * (x + y) (x(x + y) + -1y * (x + y)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 ((x * x + y * x) + -1y * (x + y)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 Reorder the terms: ((xy + x2) + -1y * (x + y)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 ((xy + x2) + -1y * (x + y)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 (xy + x2 + (x * -1y + y * -1y)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 (xy + x2 + (-1xy + -1y2)) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 Reorder the terms: (xy + -1xy + x2 + -1y2) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 Combine like terms: xy + -1xy = 0 (0 + x2 + -1y2) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 (x2 + -1y2) + -1(a + -1x + y)(a + -1x + -1y) + -1a(2x + -1a) = 0 Multiply (a + -1x + y) * (a + -1x + -1y) x2 + -1y2 + -1(a(a + -1x + -1y) + -1x * (a + -1x + -1y) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1((a * a + -1x * a + -1y * a) + -1x * (a + -1x + -1y) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 Reorder the terms: x2 + -1y2 + -1((-1ax + -1ay + a2) + -1x * (a + -1x + -1y) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1((-1ax + -1ay + a2) + -1x * (a + -1x + -1y) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-1ax + -1ay + a2 + (a * -1x + -1x * -1x + -1y * -1x) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 Reorder the terms: x2 + -1y2 + -1(-1ax + -1ay + a2 + (-1ax + 1xy + 1x2) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-1ax + -1ay + a2 + (-1ax + 1xy + 1x2) + y(a + -1x + -1y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-1ax + -1ay + a2 + -1ax + 1xy + 1x2 + (a * y + -1x * y + -1y * y)) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-1ax + -1ay + a2 + -1ax + 1xy + 1x2 + (ay + -1xy + -1y2)) + -1a(2x + -1a) = 0 Reorder the terms: x2 + -1y2 + -1(-1ax + -1ax + -1ay + ay + a2 + 1xy + -1xy + 1x2 + -1y2) + -1a(2x + -1a) = 0 Combine like terms: -1ax + -1ax = -2ax x2 + -1y2 + -1(-2ax + -1ay + ay + a2 + 1xy + -1xy + 1x2 + -1y2) + -1a(2x + -1a) = 0 Combine like terms: -1ay + ay = 0 x2 + -1y2 + -1(-2ax + 0 + a2 + 1xy + -1xy + 1x2 + -1y2) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-2ax + a2 + 1xy + -1xy + 1x2 + -1y2) + -1a(2x + -1a) = 0 Combine like terms: 1xy + -1xy = 0 x2 + -1y2 + -1(-2ax + a2 + 0 + 1x2 + -1y2) + -1a(2x + -1a) = 0 x2 + -1y2 + -1(-2ax + a2 + 1x2 + -1y2) + -1a(2x + -1a) = 0 x2 + -1y2 + (-2ax * -1 + a2 * -1 + 1x2 * -1 + -1y2 * -1) + -1a(2x + -1a) = 0 x2 + -1y2 + (2ax + -1a2 + -1x2 + 1y2) + -1a(2x + -1a) = 0 Reorder the terms: x2 + -1y2 + 2ax + -1a2 + -1x2 + 1y2 + -1a(-1a + 2x) = 0 x2 + -1y2 + 2ax + -1a2 + -1x2 + 1y2 + (-1a * -1a + 2x * -1a) = 0 Reorder the terms: x2 + -1y2 + 2ax + -1a2 + -1x2 + 1y2 + (-2ax + 1a2) = 0 x2 + -1y2 + 2ax + -1a2 + -1x2 + 1y2 + (-2ax + 1a2) = 0 Reorder the terms: 2ax + -2ax + -1a2 + 1a2 + x2 + -1x2 + -1y2 + 1y2 = 0 Combine like terms: 2ax + -2ax = 0 0 + -1a2 + 1a2 + x2 + -1x2 + -1y2 + 1y2 = 0 -1a2 + 1a2 + x2 + -1x2 + -1y2 + 1y2 = 0 Combine like terms: -1a2 + 1a2 = 0 0 + x2 + -1x2 + -1y2 + 1y2 = 0 x2 + -1x2 + -1y2 + 1y2 = 0 Combine like terms: x2 + -1x2 = 0 0 + -1y2 + 1y2 = 0 -1y2 + 1y2 = 0 Combine like terms: -1y2 + 1y2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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