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Simplifying (4x + -5y)(16x2 + kxy + 25y2) * k = 0 Reorder the terms: (4x + -5y)(kxy + 16x2 + 25y2) * k = 0 Reorder the terms for easier multiplication: k(4x + -5y)(kxy + 16x2 + 25y2) = 0 Multiply (4x + -5y) * (kxy + 16x2 + 25y2) k(4x * (kxy + 16x2 + 25y2) + -5y * (kxy + 16x2 + 25y2)) = 0 k((kxy * 4x + 16x2 * 4x + 25y2 * 4x) + -5y * (kxy + 16x2 + 25y2)) = 0 Reorder the terms: k((4kx2y + 100xy2 + 64x3) + -5y * (kxy + 16x2 + 25y2)) = 0 k((4kx2y + 100xy2 + 64x3) + -5y * (kxy + 16x2 + 25y2)) = 0 k(4kx2y + 100xy2 + 64x3 + (kxy * -5y + 16x2 * -5y + 25y2 * -5y)) = 0 k(4kx2y + 100xy2 + 64x3 + (-5kxy2 + -80x2y + -125y3)) = 0 Reorder the terms: k(-5kxy2 + 4kx2y + 100xy2 + -80x2y + 64x3 + -125y3) = 0 k(-5kxy2 + 4kx2y + 100xy2 + -80x2y + 64x3 + -125y3) = 0 (-5kxy2 * k + 4kx2y * k + 100xy2 * k + -80x2y * k + 64x3 * k + -125y3 * k) = 0 Reorder the terms: (100kxy2 + -80kx2y + 64kx3 + -125ky3 + -5k2xy2 + 4k2x2y) = 0 (100kxy2 + -80kx2y + 64kx3 + -125ky3 + -5k2xy2 + 4k2x2y) = 0 Solving 100kxy2 + -80kx2y + 64kx3 + -125ky3 + -5k2xy2 + 4k2x2y = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(100xy2 + -80x2y + 64x3 + -125y3 + -5kxy2 + 4kx2y) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(100xy2 + -80x2y + 64x3 + -125y3 + -5kxy2 + 4kx2y)' equal to zero and attempt to solve: Simplifying 100xy2 + -80x2y + 64x3 + -125y3 + -5kxy2 + 4kx2y = 0 Reorder the terms: -5kxy2 + 4kx2y + 100xy2 + -80x2y + 64x3 + -125y3 = 0 Solving -5kxy2 + 4kx2y + 100xy2 + -80x2y + 64x3 + -125y3 = 0 Move all terms containing k to the left, all other terms to the right. Add '-100xy2' to each side of the equation. -5kxy2 + 4kx2y + 100xy2 + -80x2y + 64x3 + -100xy2 + -125y3 = 0 + -100xy2 Reorder the terms: -5kxy2 + 4kx2y + 100xy2 + -100xy2 + -80x2y + 64x3 + -125y3 = 0 + -100xy2 Combine like terms: 100xy2 + -100xy2 = 0 -5kxy2 + 4kx2y + 0 + -80x2y + 64x3 + -125y3 = 0 + -100xy2 -5kxy2 + 4kx2y + -80x2y + 64x3 + -125y3 = 0 + -100xy2 Remove the zero: -5kxy2 + 4kx2y + -80x2y + 64x3 + -125y3 = -100xy2 Add '80x2y' to each side of the equation. -5kxy2 + 4kx2y + -80x2y + 64x3 + 80x2y + -125y3 = -100xy2 + 80x2y Reorder the terms: -5kxy2 + 4kx2y + -80x2y + 80x2y + 64x3 + -125y3 = -100xy2 + 80x2y Combine like terms: -80x2y + 80x2y = 0 -5kxy2 + 4kx2y + 0 + 64x3 + -125y3 = -100xy2 + 80x2y -5kxy2 + 4kx2y + 64x3 + -125y3 = -100xy2 + 80x2y Add '-64x3' to each side of the equation. -5kxy2 + 4kx2y + 64x3 + -64x3 + -125y3 = -100xy2 + 80x2y + -64x3 Combine like terms: 64x3 + -64x3 = 0 -5kxy2 + 4kx2y + 0 + -125y3 = -100xy2 + 80x2y + -64x3 -5kxy2 + 4kx2y + -125y3 = -100xy2 + 80x2y + -64x3 Add '125y3' to each side of the equation. -5kxy2 + 4kx2y + -125y3 + 125y3 = -100xy2 + 80x2y + -64x3 + 125y3 Combine like terms: -125y3 + 125y3 = 0 -5kxy2 + 4kx2y + 0 = -100xy2 + 80x2y + -64x3 + 125y3 -5kxy2 + 4kx2y = -100xy2 + 80x2y + -64x3 + 125y3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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