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Simplifying (4x + -8y)(4x + 8y) = 0 Multiply (4x + -8y) * (4x + 8y) (4x * (4x + 8y) + -8y * (4x + 8y)) = 0 ((4x * 4x + 8y * 4x) + -8y * (4x + 8y)) = 0 Reorder the terms: ((32xy + 16x2) + -8y * (4x + 8y)) = 0 ((32xy + 16x2) + -8y * (4x + 8y)) = 0 (32xy + 16x2 + (4x * -8y + 8y * -8y)) = 0 (32xy + 16x2 + (-32xy + -64y2)) = 0 Reorder the terms: (32xy + -32xy + 16x2 + -64y2) = 0 Combine like terms: 32xy + -32xy = 0 (0 + 16x2 + -64y2) = 0 (16x2 + -64y2) = 0 Solving 16x2 + -64y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '64y2' to each side of the equation. 16x2 + -64y2 + 64y2 = 0 + 64y2 Combine like terms: -64y2 + 64y2 = 0 16x2 + 0 = 0 + 64y2 16x2 = 0 + 64y2 Remove the zero: 16x2 = 64y2 Divide each side by '16'. x2 = 4y2 Simplifying x2 = 4y2 Take the square root of each side: x = {-2y, 2y}
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