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Simplifying 100n2 + -1 = (10n + 1)(10n + -1) Reorder the terms: -1 + 100n2 = (10n + 1)(10n + -1) Reorder the terms: -1 + 100n2 = (1 + 10n)(10n + -1) Reorder the terms: -1 + 100n2 = (1 + 10n)(-1 + 10n) Multiply (1 + 10n) * (-1 + 10n) -1 + 100n2 = (1(-1 + 10n) + 10n * (-1 + 10n)) -1 + 100n2 = ((-1 * 1 + 10n * 1) + 10n * (-1 + 10n)) -1 + 100n2 = ((-1 + 10n) + 10n * (-1 + 10n)) -1 + 100n2 = (-1 + 10n + (-1 * 10n + 10n * 10n)) -1 + 100n2 = (-1 + 10n + (-10n + 100n2)) Combine like terms: 10n + -10n = 0 -1 + 100n2 = (-1 + 0 + 100n2) -1 + 100n2 = (-1 + 100n2) Add '1' to each side of the equation. -1 + 1 + 100n2 = -1 + 1 + 100n2 Combine like terms: -1 + 1 = 0 0 + 100n2 = -1 + 1 + 100n2 100n2 = -1 + 1 + 100n2 Combine like terms: -1 + 1 = 0 100n2 = 0 + 100n2 100n2 = 100n2 Add '-100n2' to each side of the equation. 100n2 + -100n2 = 100n2 + -100n2 Combine like terms: 100n2 + -100n2 = 0 0 = 100n2 + -100n2 Combine like terms: 100n2 + -100n2 = 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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