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Simplifying (2a2 + -8)(4a4 + 16a2 + 64) = 0 Reorder the terms: (-8 + 2a2)(4a4 + 16a2 + 64) = 0 Reorder the terms: (-8 + 2a2)(64 + 16a2 + 4a4) = 0 Multiply (-8 + 2a2) * (64 + 16a2 + 4a4) (-8(64 + 16a2 + 4a4) + 2a2 * (64 + 16a2 + 4a4)) = 0 ((64 * -8 + 16a2 * -8 + 4a4 * -8) + 2a2 * (64 + 16a2 + 4a4)) = 0 ((-512 + -128a2 + -32a4) + 2a2 * (64 + 16a2 + 4a4)) = 0 (-512 + -128a2 + -32a4 + (64 * 2a2 + 16a2 * 2a2 + 4a4 * 2a2)) = 0 (-512 + -128a2 + -32a4 + (128a2 + 32a4 + 8a6)) = 0 Reorder the terms: (-512 + -128a2 + 128a2 + -32a4 + 32a4 + 8a6) = 0 Combine like terms: -128a2 + 128a2 = 0 (-512 + 0 + -32a4 + 32a4 + 8a6) = 0 (-512 + -32a4 + 32a4 + 8a6) = 0 Combine like terms: -32a4 + 32a4 = 0 (-512 + 0 + 8a6) = 0 (-512 + 8a6) = 0 Solving -512 + 8a6 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '512' to each side of the equation. -512 + 512 + 8a6 = 0 + 512 Combine like terms: -512 + 512 = 0 0 + 8a6 = 0 + 512 8a6 = 0 + 512 Combine like terms: 0 + 512 = 512 8a6 = 512 Divide each side by '8'. a6 = 64 Simplifying a6 = 64 Reorder the terms: -64 + a6 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + a6 = 0 Factor a difference between two squares. (8 + a3)(-8 + a3) = 0Subproblem 1
Set the factor '(8 + a3)' equal to zero and attempt to solve: Simplifying 8 + a3 = 0 Solving 8 + a3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + a3 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + a3 = 0 + -8 a3 = 0 + -8 Combine like terms: 0 + -8 = -8 a3 = -8 Simplifying a3 = -8 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 '(-8 + a3)' equal to zero and attempt to solve: Simplifying -8 + a3 = 0 Solving -8 + a3 = 0 Move all terms containing a to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + a3 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + a3 = 0 + 8 a3 = 0 + 8 Combine like terms: 0 + 8 = 8 a3 = 8 Simplifying a3 = 8 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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