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Simplifying (2a + b)(4a2 + -2ab + b2)(8a3 + -1b3) = 0 Reorder the terms: (2a + b)(-2ab + 4a2 + b2)(8a3 + -1b3) = 0 Multiply (2a + b) * (-2ab + 4a2 + b2) (2a * (-2ab + 4a2 + b2) + b(-2ab + 4a2 + b2))(8a3 + -1b3) = 0 ((-2ab * 2a + 4a2 * 2a + b2 * 2a) + b(-2ab + 4a2 + b2))(8a3 + -1b3) = 0 Reorder the terms: ((2ab2 + -4a2b + 8a3) + b(-2ab + 4a2 + b2))(8a3 + -1b3) = 0 ((2ab2 + -4a2b + 8a3) + b(-2ab + 4a2 + b2))(8a3 + -1b3) = 0 (2ab2 + -4a2b + 8a3 + (-2ab * b + 4a2 * b + b2 * b))(8a3 + -1b3) = 0 (2ab2 + -4a2b + 8a3 + (-2ab2 + 4a2b + b3))(8a3 + -1b3) = 0 Reorder the terms: (2ab2 + -2ab2 + -4a2b + 4a2b + 8a3 + b3)(8a3 + -1b3) = 0 Combine like terms: 2ab2 + -2ab2 = 0 (0 + -4a2b + 4a2b + 8a3 + b3)(8a3 + -1b3) = 0 (-4a2b + 4a2b + 8a3 + b3)(8a3 + -1b3) = 0 Combine like terms: -4a2b + 4a2b = 0 (0 + 8a3 + b3)(8a3 + -1b3) = 0 (8a3 + b3)(8a3 + -1b3) = 0 Multiply (8a3 + b3) * (8a3 + -1b3) (8a3 * (8a3 + -1b3) + b3(8a3 + -1b3)) = 0 ((8a3 * 8a3 + -1b3 * 8a3) + b3(8a3 + -1b3)) = 0 Reorder the terms: ((-8a3b3 + 64a6) + b3(8a3 + -1b3)) = 0 ((-8a3b3 + 64a6) + b3(8a3 + -1b3)) = 0 (-8a3b3 + 64a6 + (8a3 * b3 + -1b3 * b3)) = 0 (-8a3b3 + 64a6 + (8a3b3 + -1b6)) = 0 Reorder the terms: (-8a3b3 + 8a3b3 + 64a6 + -1b6) = 0 Combine like terms: -8a3b3 + 8a3b3 = 0 (0 + 64a6 + -1b6) = 0 (64a6 + -1b6) = 0 Solving 64a6 + -1b6 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add 'b6' to each side of the equation. 64a6 + -1b6 + b6 = 0 + b6 Combine like terms: -1b6 + b6 = 0 64a6 + 0 = 0 + b6 64a6 = 0 + b6 Remove the zero: 64a6 = b6 Divide each side by '64'. a6 = 0.015625b6 Simplifying a6 = 0.015625b6 Combine like terms: 0.015625b6 + -0.015625b6 = 0.000000 a6 + -0.015625b6 = 0.000000 Factor a difference between two squares. (a3 + 0.125b3)(a3 + -0.125b3) = 0.000000Subproblem 1
Set the factor '(a3 + 0.125b3)' equal to zero and attempt to solve: Simplifying a3 + 0.125b3 = 0 Solving a3 + 0.125b3 = 0 Move all terms containing a to the left, all other terms to the right. Add '-0.125b3' to each side of the equation. a3 + 0.125b3 + -0.125b3 = 0 + -0.125b3 Combine like terms: 0.125b3 + -0.125b3 = 0.000 a3 + 0.000 = 0 + -0.125b3 a3 = 0 + -0.125b3 Remove the zero: a3 = -0.125b3 Simplifying a3 = -0.125b3 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 '(a3 + -0.125b3)' equal to zero and attempt to solve: Simplifying a3 + -0.125b3 = 0 Solving a3 + -0.125b3 = 0 Move all terms containing a to the left, all other terms to the right. Add '0.125b3' to each side of the equation. a3 + -0.125b3 + 0.125b3 = 0 + 0.125b3 Combine like terms: -0.125b3 + 0.125b3 = 0.000 a3 + 0.000 = 0 + 0.125b3 a3 = 0 + 0.125b3 Remove the zero: a3 = 0.125b3 Simplifying a3 = 0.125b3 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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