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Simplifying (4ab3 + a2b4)(3a2b4 + -4ab3) = 0 Reorder the terms: (4ab3 + a2b4)(-4ab3 + 3a2b4) = 0 Multiply (4ab3 + a2b4) * (-4ab3 + 3a2b4) (4ab3 * (-4ab3 + 3a2b4) + a2b4(-4ab3 + 3a2b4)) = 0 ((-4ab3 * 4ab3 + 3a2b4 * 4ab3) + a2b4(-4ab3 + 3a2b4)) = 0 ((-16a2b6 + 12a3b7) + a2b4(-4ab3 + 3a2b4)) = 0 (-16a2b6 + 12a3b7 + (-4ab3 * a2b4 + 3a2b4 * a2b4)) = 0 (-16a2b6 + 12a3b7 + (-4a3b7 + 3a4b8)) = 0 Combine like terms: 12a3b7 + -4a3b7 = 8a3b7 (-16a2b6 + 8a3b7 + 3a4b8) = 0 Solving -16a2b6 + 8a3b7 + 3a4b8 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a2b6'. a2b6(-16 + 8ab + 3a2b2) = 0 Factor a trinomial. a2b6((-4 + -1ab)(4 + -3ab)) = 0Subproblem 1
Set the factor 'a2b6' equal to zero and attempt to solve: Simplifying a2b6 = 0 Solving a2b6 = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a2b6 = 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 '(-4 + -1ab)' equal to zero and attempt to solve: Simplifying -4 + -1ab = 0 Solving -4 + -1ab = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1ab = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1ab = 0 + 4 -1ab = 0 + 4 Combine like terms: 0 + 4 = 4 -1ab = 4 Divide each side by '-1b'. a = -4b-1 Simplifying a = -4b-1Subproblem 3
Set the factor '(4 + -3ab)' equal to zero and attempt to solve: Simplifying 4 + -3ab = 0 Solving 4 + -3ab = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3ab = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3ab = 0 + -4 -3ab = 0 + -4 Combine like terms: 0 + -4 = -4 -3ab = -4 Divide each side by '-3b'. a = 1.333333333b-1 Simplifying a = 1.333333333b-1Solution
a = {-4b-1, 1.333333333b-1}
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