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Simplifying 25x2 + -1y2 = (5x + -1y)(5x + y) Multiply (5x + -1y) * (5x + y) 25x2 + -1y2 = (5x * (5x + y) + -1y * (5x + y)) 25x2 + -1y2 = ((5x * 5x + y * 5x) + -1y * (5x + y)) Reorder the terms: 25x2 + -1y2 = ((5xy + 25x2) + -1y * (5x + y)) 25x2 + -1y2 = ((5xy + 25x2) + -1y * (5x + y)) 25x2 + -1y2 = (5xy + 25x2 + (5x * -1y + y * -1y)) 25x2 + -1y2 = (5xy + 25x2 + (-5xy + -1y2)) Reorder the terms: 25x2 + -1y2 = (5xy + -5xy + 25x2 + -1y2) Combine like terms: 5xy + -5xy = 0 25x2 + -1y2 = (0 + 25x2 + -1y2) 25x2 + -1y2 = (25x2 + -1y2) Add '-25x2' to each side of the equation. 25x2 + -25x2 + -1y2 = 25x2 + -25x2 + -1y2 Combine like terms: 25x2 + -25x2 = 0 0 + -1y2 = 25x2 + -25x2 + -1y2 -1y2 = 25x2 + -25x2 + -1y2 Combine like terms: 25x2 + -25x2 = 0 -1y2 = 0 + -1y2 -1y2 = -1y2 Add 'y2' to each side of the equation. -1y2 + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 0 = -1y2 + y2 Combine like terms: -1y2 + y2 = 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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