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Simplifying (a2 + 4ab + -5b2)(a2 + -4ab + -5b2) = 0 Reorder the terms: (4ab + a2 + -5b2)(a2 + -4ab + -5b2) = 0 Reorder the terms: (4ab + a2 + -5b2)(-4ab + a2 + -5b2) = 0 Multiply (4ab + a2 + -5b2) * (-4ab + a2 + -5b2) (4ab * (-4ab + a2 + -5b2) + a2(-4ab + a2 + -5b2) + -5b2 * (-4ab + a2 + -5b2)) = 0 ((-4ab * 4ab + a2 * 4ab + -5b2 * 4ab) + a2(-4ab + a2 + -5b2) + -5b2 * (-4ab + a2 + -5b2)) = 0 Reorder the terms: ((-20ab3 + -16a2b2 + 4a3b) + a2(-4ab + a2 + -5b2) + -5b2 * (-4ab + a2 + -5b2)) = 0 ((-20ab3 + -16a2b2 + 4a3b) + a2(-4ab + a2 + -5b2) + -5b2 * (-4ab + a2 + -5b2)) = 0 (-20ab3 + -16a2b2 + 4a3b + (-4ab * a2 + a2 * a2 + -5b2 * a2) + -5b2 * (-4ab + a2 + -5b2)) = 0 Reorder the terms: (-20ab3 + -16a2b2 + 4a3b + (-5a2b2 + -4a3b + a4) + -5b2 * (-4ab + a2 + -5b2)) = 0 (-20ab3 + -16a2b2 + 4a3b + (-5a2b2 + -4a3b + a4) + -5b2 * (-4ab + a2 + -5b2)) = 0 (-20ab3 + -16a2b2 + 4a3b + -5a2b2 + -4a3b + a4 + (-4ab * -5b2 + a2 * -5b2 + -5b2 * -5b2)) = 0 (-20ab3 + -16a2b2 + 4a3b + -5a2b2 + -4a3b + a4 + (20ab3 + -5a2b2 + 25b4)) = 0 Reorder the terms: (-20ab3 + 20ab3 + -16a2b2 + -5a2b2 + -5a2b2 + 4a3b + -4a3b + a4 + 25b4) = 0 Combine like terms: -20ab3 + 20ab3 = 0 (0 + -16a2b2 + -5a2b2 + -5a2b2 + 4a3b + -4a3b + a4 + 25b4) = 0 (-16a2b2 + -5a2b2 + -5a2b2 + 4a3b + -4a3b + a4 + 25b4) = 0 Combine like terms: -16a2b2 + -5a2b2 = -21a2b2 (-21a2b2 + -5a2b2 + 4a3b + -4a3b + a4 + 25b4) = 0 Combine like terms: -21a2b2 + -5a2b2 = -26a2b2 (-26a2b2 + 4a3b + -4a3b + a4 + 25b4) = 0 Combine like terms: 4a3b + -4a3b = 0 (-26a2b2 + 0 + a4 + 25b4) = 0 (-26a2b2 + a4 + 25b4) = 0 Solving -26a2b2 + a4 + 25b4 = 0 Solving for variable 'a'. Factor a trinomial. (a2 + -25b2)(a2 + -1b2) = 0 Factor a difference between two squares. ((a + 5b)(a + -5b))(a2 + -1b2) = 0 Factor a difference between two squares. ((a + b)(a + -1b))(a + 5b)(a + -5b) = 0Subproblem 1
Set the factor '(a + 5b)' equal to zero and attempt to solve: Simplifying a + 5b = 0 Solving a + 5b = 0 Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. a + 5b + -5b = 0 + -5b Combine like terms: 5b + -5b = 0 a + 0 = 0 + -5b a = 0 + -5b Remove the zero: a = -5b Simplifying a = -5bSubproblem 2
Set the factor '(a + -5b)' equal to zero and attempt to solve: Simplifying a + -5b = 0 Solving a + -5b = 0 Move all terms containing a to the left, all other terms to the right. Add '5b' to each side of the equation. a + -5b + 5b = 0 + 5b Combine like terms: -5b + 5b = 0 a + 0 = 0 + 5b a = 0 + 5b Remove the zero: a = 5b Simplifying a = 5bSubproblem 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 = {-5b, 5b, -1b, b}
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