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Simplifying (x + y2)(4x + -8y2) = 0 Multiply (x + y2) * (4x + -8y2) (x(4x + -8y2) + y2(4x + -8y2)) = 0 ((4x * x + -8y2 * x) + y2(4x + -8y2)) = 0 Reorder the terms: ((-8xy2 + 4x2) + y2(4x + -8y2)) = 0 ((-8xy2 + 4x2) + y2(4x + -8y2)) = 0 (-8xy2 + 4x2 + (4x * y2 + -8y2 * y2)) = 0 (-8xy2 + 4x2 + (4xy2 + -8y4)) = 0 Reorder the terms: (-8xy2 + 4xy2 + 4x2 + -8y4) = 0 Combine like terms: -8xy2 + 4xy2 = -4xy2 (-4xy2 + 4x2 + -8y4) = 0 Solving -4xy2 + 4x2 + -8y4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1xy2 + x2 + -2y4) = 0 Factor a trinomial. 4((x + -2y2)(x + y2)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(x + -2y2)' equal to zero and attempt to solve: Simplifying x + -2y2 = 0 Solving x + -2y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '2y2' to each side of the equation. x + -2y2 + 2y2 = 0 + 2y2 Combine like terms: -2y2 + 2y2 = 0 x + 0 = 0 + 2y2 x = 0 + 2y2 Remove the zero: x = 2y2 Simplifying x = 2y2Subproblem 2
Set the factor '(x + y2)' equal to zero and attempt to solve: Simplifying x + y2 = 0 Solving x + y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. x + y2 + -1y2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 x + 0 = 0 + -1y2 x = 0 + -1y2 Remove the zero: x = -1y2 Simplifying x = -1y2Solution
x = {2y2, -1y2}
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