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Simplifying 9a3bx + 12a2b2x + -5ab3x = abx(3a + 5b)(3a + -1b) Reorder the terms: -5ab3x + 12a2b2x + 9a3bx = abx(3a + 5b)(3a + -1b) Multiply (3a + 5b) * (3a + -1b) -5ab3x + 12a2b2x + 9a3bx = abx(3a * (3a + -1b) + 5b * (3a + -1b)) -5ab3x + 12a2b2x + 9a3bx = abx((3a * 3a + -1b * 3a) + 5b * (3a + -1b)) Reorder the terms: -5ab3x + 12a2b2x + 9a3bx = abx((-3ab + 9a2) + 5b * (3a + -1b)) -5ab3x + 12a2b2x + 9a3bx = abx((-3ab + 9a2) + 5b * (3a + -1b)) -5ab3x + 12a2b2x + 9a3bx = abx(-3ab + 9a2 + (3a * 5b + -1b * 5b)) -5ab3x + 12a2b2x + 9a3bx = abx(-3ab + 9a2 + (15ab + -5b2)) Reorder the terms: -5ab3x + 12a2b2x + 9a3bx = abx(-3ab + 15ab + 9a2 + -5b2) Combine like terms: -3ab + 15ab = 12ab -5ab3x + 12a2b2x + 9a3bx = abx(12ab + 9a2 + -5b2) -5ab3x + 12a2b2x + 9a3bx = (12ab * abx + 9a2 * abx + -5b2 * abx) Reorder the terms: -5ab3x + 12a2b2x + 9a3bx = (-5ab3x + 12a2b2x + 9a3bx) -5ab3x + 12a2b2x + 9a3bx = (-5ab3x + 12a2b2x + 9a3bx) Add '5ab3x' to each side of the equation. -5ab3x + 12a2b2x + 5ab3x + 9a3bx = -5ab3x + 12a2b2x + 5ab3x + 9a3bx Reorder the terms: -5ab3x + 5ab3x + 12a2b2x + 9a3bx = -5ab3x + 12a2b2x + 5ab3x + 9a3bx Combine like terms: -5ab3x + 5ab3x = 0 0 + 12a2b2x + 9a3bx = -5ab3x + 12a2b2x + 5ab3x + 9a3bx 12a2b2x + 9a3bx = -5ab3x + 12a2b2x + 5ab3x + 9a3bx Reorder the terms: 12a2b2x + 9a3bx = -5ab3x + 5ab3x + 12a2b2x + 9a3bx Combine like terms: -5ab3x + 5ab3x = 0 12a2b2x + 9a3bx = 0 + 12a2b2x + 9a3bx 12a2b2x + 9a3bx = 12a2b2x + 9a3bx Add '-12a2b2x' to each side of the equation. 12a2b2x + -12a2b2x + 9a3bx = 12a2b2x + -12a2b2x + 9a3bx Combine like terms: 12a2b2x + -12a2b2x = 0 0 + 9a3bx = 12a2b2x + -12a2b2x + 9a3bx 9a3bx = 12a2b2x + -12a2b2x + 9a3bx Combine like terms: 12a2b2x + -12a2b2x = 0 9a3bx = 0 + 9a3bx 9a3bx = 9a3bx Add '-9a3bx' to each side of the equation. 9a3bx + -9a3bx = 9a3bx + -9a3bx Combine like terms: 9a3bx + -9a3bx = 0 0 = 9a3bx + -9a3bx Combine like terms: 9a3bx + -9a3bx = 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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