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Simplifying a4b4 + -16 = 0 Reorder the terms: -16 + a4b4 = 0 Solving -16 + a4b4 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + a4b4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + a4b4 = 0 + 16 a4b4 = 0 + 16 Combine like terms: 0 + 16 = 16 a4b4 = 16 Divide each side by 'b4'. a4 = 16b-4 Simplifying a4 = 16b-4 Combine like terms: 16b-4 + -16b-4 = 0 a4 + -16b-4 = 0 Factor out the Greatest Common Factor (GCF), 'b-4'. b-4(a4b4 + -16) = 0 Factor a difference between two squares. b-4((a2b2 + 4)(a2b2 + -4)) = 0 Factor a difference between two squares. b-4((a2b2 + 4)((ab + 2)(ab + -2))) = 0Subproblem 1
Set the factor 'b-4' equal to zero and attempt to solve: Simplifying b-4 = 0 Solving b-4 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b-4' to each side of the equation. b-4 + -1b-4 = 0 + -1b-4 Remove the zero: 0 = -1b-4 Simplifying 0 = -1b-4 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 '(a2b2 + 4)' equal to zero and attempt to solve: Simplifying a2b2 + 4 = 0 Reorder the terms: 4 + a2b2 = 0 Solving 4 + a2b2 = 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 + a2b2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a2b2 = 0 + -4 a2b2 = 0 + -4 Combine like terms: 0 + -4 = -4 a2b2 = -4 Divide each side by 'b2'. a2 = -4b-2 Simplifying a2 = -4b-2 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 '(ab + 2)' equal to zero and attempt to solve: Simplifying ab + 2 = 0 Reorder the terms: 2 + ab = 0 Solving 2 + ab = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + ab = 0 + -2 Combine like terms: 2 + -2 = 0 0 + ab = 0 + -2 ab = 0 + -2 Combine like terms: 0 + -2 = -2 ab = -2 Divide each side by 'b'. a = -2b-1 Simplifying a = -2b-1Subproblem 4
Set the factor '(ab + -2)' equal to zero and attempt to solve: Simplifying ab + -2 = 0 Reorder the terms: -2 + ab = 0 Solving -2 + ab = 0 Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + ab = 0 + 2 Combine like terms: -2 + 2 = 0 0 + ab = 0 + 2 ab = 0 + 2 Combine like terms: 0 + 2 = 2 ab = 2 Divide each side by 'b'. a = 2b-1 Simplifying a = 2b-1Solution
a = {-2b-1, 2b-1}
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