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Simplifying (t + x + y)(t + -1x + -1y) = 0 Multiply (t + x + y) * (t + -1x + -1y) (t(t + -1x + -1y) + x(t + -1x + -1y) + y(t + -1x + -1y)) = 0 ((t * t + -1x * t + -1y * t) + x(t + -1x + -1y) + y(t + -1x + -1y)) = 0 Reorder the terms: ((-1tx + -1ty + t2) + x(t + -1x + -1y) + y(t + -1x + -1y)) = 0 ((-1tx + -1ty + t2) + x(t + -1x + -1y) + y(t + -1x + -1y)) = 0 (-1tx + -1ty + t2 + (t * x + -1x * x + -1y * x) + y(t + -1x + -1y)) = 0 Reorder the terms: (-1tx + -1ty + t2 + (tx + -1xy + -1x2) + y(t + -1x + -1y)) = 0 (-1tx + -1ty + t2 + (tx + -1xy + -1x2) + y(t + -1x + -1y)) = 0 (-1tx + -1ty + t2 + tx + -1xy + -1x2 + (t * y + -1x * y + -1y * y)) = 0 (-1tx + -1ty + t2 + tx + -1xy + -1x2 + (ty + -1xy + -1y2)) = 0 Reorder the terms: (-1tx + tx + -1ty + ty + t2 + -1xy + -1xy + -1x2 + -1y2) = 0 Combine like terms: -1tx + tx = 0 (0 + -1ty + ty + t2 + -1xy + -1xy + -1x2 + -1y2) = 0 (-1ty + ty + t2 + -1xy + -1xy + -1x2 + -1y2) = 0 Combine like terms: -1ty + ty = 0 (0 + t2 + -1xy + -1xy + -1x2 + -1y2) = 0 (t2 + -1xy + -1xy + -1x2 + -1y2) = 0 Combine like terms: -1xy + -1xy = -2xy (t2 + -2xy + -1x2 + -1y2) = 0 Solving t2 + -2xy + -1x2 + -1y2 = 0 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2xy' to each side of the equation. t2 + -2xy + -1x2 + 2xy + -1y2 = 0 + 2xy Reorder the terms: t2 + -2xy + 2xy + -1x2 + -1y2 = 0 + 2xy Combine like terms: -2xy + 2xy = 0 t2 + 0 + -1x2 + -1y2 = 0 + 2xy t2 + -1x2 + -1y2 = 0 + 2xy Remove the zero: t2 + -1x2 + -1y2 = 2xy Add 'x2' to each side of the equation. t2 + -1x2 + x2 + -1y2 = 2xy + x2 Combine like terms: -1x2 + x2 = 0 t2 + 0 + -1y2 = 2xy + x2 t2 + -1y2 = 2xy + x2 Add 'y2' to each side of the equation. t2 + -1y2 + y2 = 2xy + x2 + y2 Combine like terms: -1y2 + y2 = 0 t2 + 0 = 2xy + x2 + y2 t2 = 2xy + x2 + y2 Simplifying t2 = 2xy + x2 + y2 Reorder the terms: t2 + -2xy + -1x2 + -1y2 = 2xy + -2xy + x2 + -1x2 + y2 + -1y2 Combine like terms: 2xy + -2xy = 0 t2 + -2xy + -1x2 + -1y2 = 0 + x2 + -1x2 + y2 + -1y2 t2 + -2xy + -1x2 + -1y2 = x2 + -1x2 + y2 + -1y2 Combine like terms: x2 + -1x2 = 0 t2 + -2xy + -1x2 + -1y2 = 0 + y2 + -1y2 t2 + -2xy + -1x2 + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 t2 + -2xy + -1x2 + -1y2 = 0 The solution to this equation could not be determined.
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