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Simplifying (y + -1)(8 + -1y) = 16 + -1(y + -2)(y + -2) Reorder the terms: (-1 + y)(8 + -1y) = 16 + -1(y + -2)(y + -2) Multiply (-1 + y) * (8 + -1y) (-1(8 + -1y) + y(8 + -1y)) = 16 + -1(y + -2)(y + -2) ((8 * -1 + -1y * -1) + y(8 + -1y)) = 16 + -1(y + -2)(y + -2) ((-8 + 1y) + y(8 + -1y)) = 16 + -1(y + -2)(y + -2) (-8 + 1y + (8 * y + -1y * y)) = 16 + -1(y + -2)(y + -2) (-8 + 1y + (8y + -1y2)) = 16 + -1(y + -2)(y + -2) Combine like terms: 1y + 8y = 9y (-8 + 9y + -1y2) = 16 + -1(y + -2)(y + -2) Reorder the terms: -8 + 9y + -1y2 = 16 + -1(-2 + y)(y + -2) Reorder the terms: -8 + 9y + -1y2 = 16 + -1(-2 + y)(-2 + y) Multiply (-2 + y) * (-2 + y) -8 + 9y + -1y2 = 16 + -1(-2(-2 + y) + y(-2 + y)) -8 + 9y + -1y2 = 16 + -1((-2 * -2 + y * -2) + y(-2 + y)) -8 + 9y + -1y2 = 16 + -1((4 + -2y) + y(-2 + y)) -8 + 9y + -1y2 = 16 + -1(4 + -2y + (-2 * y + y * y)) -8 + 9y + -1y2 = 16 + -1(4 + -2y + (-2y + y2)) Combine like terms: -2y + -2y = -4y -8 + 9y + -1y2 = 16 + -1(4 + -4y + y2) -8 + 9y + -1y2 = 16 + (4 * -1 + -4y * -1 + y2 * -1) -8 + 9y + -1y2 = 16 + (-4 + 4y + -1y2) Combine like terms: 16 + -4 = 12 -8 + 9y + -1y2 = 12 + 4y + -1y2 Add 'y2' to each side of the equation. -8 + 9y + -1y2 + y2 = 12 + 4y + -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -8 + 9y + 0 = 12 + 4y + -1y2 + y2 -8 + 9y = 12 + 4y + -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -8 + 9y = 12 + 4y + 0 -8 + 9y = 12 + 4y Solving -8 + 9y = 12 + 4y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4y' to each side of the equation. -8 + 9y + -4y = 12 + 4y + -4y Combine like terms: 9y + -4y = 5y -8 + 5y = 12 + 4y + -4y Combine like terms: 4y + -4y = 0 -8 + 5y = 12 + 0 -8 + 5y = 12 Add '8' to each side of the equation. -8 + 8 + 5y = 12 + 8 Combine like terms: -8 + 8 = 0 0 + 5y = 12 + 8 5y = 12 + 8 Combine like terms: 12 + 8 = 20 5y = 20 Divide each side by '5'. y = 4 Simplifying y = 4
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