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Simplifying f(x + y + -1xy) = f(x) + f(y) + -1f(xy) Reorder the terms: f(x + -1xy + y) = f(x) + f(y) + -1f(xy) (x * f + -1xy * f + y * f) = f(x) + f(y) + -1f(xy) (fx + -1fxy + fy) = f(x) + f(y) + -1f(xy) Multiply f * x fx + -1fxy + fy = fx + f(y) + -1f(xy) Multiply f * y fx + -1fxy + fy = fx + fy + -1f(xy) Multiply f * xy fx + -1fxy + fy = fx + fy + -1fxy Reorder the terms: fx + -1fxy + fy = fx + -1fxy + fy Add '-1fx' to each side of the equation. fx + -1fxy + -1fx + fy = fx + -1fxy + -1fx + fy Reorder the terms: fx + -1fx + -1fxy + fy = fx + -1fxy + -1fx + fy Combine like terms: fx + -1fx = 0 0 + -1fxy + fy = fx + -1fxy + -1fx + fy -1fxy + fy = fx + -1fxy + -1fx + fy Reorder the terms: -1fxy + fy = fx + -1fx + -1fxy + fy Combine like terms: fx + -1fx = 0 -1fxy + fy = 0 + -1fxy + fy -1fxy + fy = -1fxy + fy Add 'fxy' to each side of the equation. -1fxy + fxy + fy = -1fxy + fxy + fy Combine like terms: -1fxy + fxy = 0 0 + fy = -1fxy + fxy + fy fy = -1fxy + fxy + fy Combine like terms: -1fxy + fxy = 0 fy = 0 + fy fy = fy Add '-1fy' to each side of the equation. fy + -1fy = fy + -1fy Combine like terms: fy + -1fy = 0 0 = fy + -1fy Combine like terms: fy + -1fy = 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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