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Simplifying 24x4 + -81xy3 = 3x4(2 + -3xy)(4 + 6xy + 9x2y2) Reorder the terms: -81xy3 + 24x4 = 3x4(2 + -3xy)(4 + 6xy + 9x2y2) Multiply (2 + -3xy) * (4 + 6xy + 9x2y2) -81xy3 + 24x4 = 3x4(2(4 + 6xy + 9x2y2) + -3xy * (4 + 6xy + 9x2y2)) -81xy3 + 24x4 = 3x4((4 * 2 + 6xy * 2 + 9x2y2 * 2) + -3xy * (4 + 6xy + 9x2y2)) -81xy3 + 24x4 = 3x4((8 + 12xy + 18x2y2) + -3xy * (4 + 6xy + 9x2y2)) -81xy3 + 24x4 = 3x4(8 + 12xy + 18x2y2 + (4 * -3xy + 6xy * -3xy + 9x2y2 * -3xy)) -81xy3 + 24x4 = 3x4(8 + 12xy + 18x2y2 + (-12xy + -18x2y2 + -27x3y3)) Reorder the terms: -81xy3 + 24x4 = 3x4(8 + 12xy + -12xy + 18x2y2 + -18x2y2 + -27x3y3) Combine like terms: 12xy + -12xy = 0 -81xy3 + 24x4 = 3x4(8 + 0 + 18x2y2 + -18x2y2 + -27x3y3) -81xy3 + 24x4 = 3x4(8 + 18x2y2 + -18x2y2 + -27x3y3) Combine like terms: 18x2y2 + -18x2y2 = 0 -81xy3 + 24x4 = 3x4(8 + 0 + -27x3y3) -81xy3 + 24x4 = 3x4(8 + -27x3y3) -81xy3 + 24x4 = (8 * 3x4 + -27x3y3 * 3x4) -81xy3 + 24x4 = (24x4 + -81x7y3) Add '-24x4' to each side of the equation. -81xy3 + 24x4 + -24x4 = 24x4 + -24x4 + -81x7y3 Combine like terms: 24x4 + -24x4 = 0 -81xy3 + 0 = 24x4 + -24x4 + -81x7y3 -81xy3 = 24x4 + -24x4 + -81x7y3 Combine like terms: 24x4 + -24x4 = 0 -81xy3 = 0 + -81x7y3 -81xy3 = -81x7y3 Solving -81xy3 = -81x7y3 Solving for variable 'x'. Combine like terms: -81x7y3 + 81x7y3 = 0 -81xy3 + 81x7y3 = 0 Factor out the Greatest Common Factor (GCF), '81xy3'. 81xy3(-1 + x6) = 0 Factor a difference between two squares. 81xy3((1 + x3)(-1 + x3)) = 0 Ignore the factor 81.Subproblem 1
Set the factor 'xy3' equal to zero and attempt to solve: Simplifying xy3 = 0 Solving xy3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying xy3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + x3)' equal to zero and attempt to solve: Simplifying 1 + x3 = 0 Solving 1 + x3 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x3 = 0 + -1 x3 = 0 + -1 Combine like terms: 0 + -1 = -1 x3 = -1 Simplifying x3 = -1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(-1 + x3)' equal to zero and attempt to solve: Simplifying -1 + x3 = 0 Solving -1 + x3 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x3 = 0 + 1 x3 = 0 + 1 Combine like terms: 0 + 1 = 1 x3 = 1 Simplifying x3 = 1 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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