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Simplifying a4 + -2a2b2 + b4 = 0 Reorder the terms: -2a2b2 + a4 + b4 = 0 Solving -2a2b2 + a4 + b4 = 0 Solving for variable 'a'. Factor a trinomial. (a2 + -1b2)(a2 + -1b2) = 0 Factor a difference between two squares. ((a + b)(a + -1b))(a2 + -1b2) = 0 Factor a difference between two squares. ((a + b)(a + -1b))(a + b)(a + -1b) = 0Subproblem 1
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 2
Set the factor '(a + -1b)' equal to zero and attempt to solve: Simplifying a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = bSubproblem 3
Set the factor '(a + b)' equal to zero and attempt to solve: Simplifying a + b = 0 Solving a + b = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b = 0 + -1b Combine like terms: b + -1b = 0 a + 0 = 0 + -1b a = 0 + -1b Remove the zero: a = -1b Simplifying a = -1bSubproblem 4
Set the factor '(a + -1b)' equal to zero and attempt to solve: Simplifying a + -1b = 0 Solving a + -1b = 0 Move all terms containing a to the left, all other terms to the right. Add 'b' to each side of the equation. a + -1b + b = 0 + b Combine like terms: -1b + b = 0 a + 0 = 0 + b a = 0 + b Remove the zero: a = b Simplifying a = bSolution
a = {-1b, b, -1b, b}
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