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Simplifying (5x + 1)(25x2 + -5x + 1) = 125x3 + 1 Reorder the terms: (1 + 5x)(25x2 + -5x + 1) = 125x3 + 1 Reorder the terms: (1 + 5x)(1 + -5x + 25x2) = 125x3 + 1 Multiply (1 + 5x) * (1 + -5x + 25x2) (1(1 + -5x + 25x2) + 5x * (1 + -5x + 25x2)) = 125x3 + 1 ((1 * 1 + -5x * 1 + 25x2 * 1) + 5x * (1 + -5x + 25x2)) = 125x3 + 1 ((1 + -5x + 25x2) + 5x * (1 + -5x + 25x2)) = 125x3 + 1 (1 + -5x + 25x2 + (1 * 5x + -5x * 5x + 25x2 * 5x)) = 125x3 + 1 (1 + -5x + 25x2 + (5x + -25x2 + 125x3)) = 125x3 + 1 Reorder the terms: (1 + -5x + 5x + 25x2 + -25x2 + 125x3) = 125x3 + 1 Combine like terms: -5x + 5x = 0 (1 + 0 + 25x2 + -25x2 + 125x3) = 125x3 + 1 (1 + 25x2 + -25x2 + 125x3) = 125x3 + 1 Combine like terms: 25x2 + -25x2 = 0 (1 + 0 + 125x3) = 125x3 + 1 (1 + 125x3) = 125x3 + 1 Reorder the terms: 1 + 125x3 = 1 + 125x3 Add '-1' to each side of the equation. 1 + -1 + 125x3 = 1 + -1 + 125x3 Combine like terms: 1 + -1 = 0 0 + 125x3 = 1 + -1 + 125x3 125x3 = 1 + -1 + 125x3 Combine like terms: 1 + -1 = 0 125x3 = 0 + 125x3 125x3 = 125x3 Add '-125x3' to each side of the equation. 125x3 + -125x3 = 125x3 + -125x3 Combine like terms: 125x3 + -125x3 = 0 0 = 125x3 + -125x3 Combine like terms: 125x3 + -125x3 = 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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