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Simplifying (a + 10)(b + -10) = a * b + -20 Reorder the terms: (10 + a)(b + -10) = a * b + -20 Reorder the terms: (10 + a)(-10 + b) = a * b + -20 Multiply (10 + a) * (-10 + b) (10(-10 + b) + a(-10 + b)) = a * b + -20 ((-10 * 10 + b * 10) + a(-10 + b)) = a * b + -20 ((-100 + 10b) + a(-10 + b)) = a * b + -20 (-100 + 10b + (-10 * a + b * a)) = a * b + -20 (-100 + 10b + (-10a + ab)) = a * b + -20 Reorder the terms: (-100 + -10a + ab + 10b) = a * b + -20 (-100 + -10a + ab + 10b) = a * b + -20 Multiply a * b -100 + -10a + ab + 10b = ab + -20 Reorder the terms: -100 + -10a + ab + 10b = -20 + ab Add '-1ab' to each side of the equation. -100 + -10a + ab + -1ab + 10b = -20 + ab + -1ab Combine like terms: ab + -1ab = 0 -100 + -10a + 0 + 10b = -20 + ab + -1ab -100 + -10a + 10b = -20 + ab + -1ab Combine like terms: ab + -1ab = 0 -100 + -10a + 10b = -20 + 0 -100 + -10a + 10b = -20 Solving -100 + -10a + 10b = -20 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '100' to each side of the equation. -100 + -10a + 100 + 10b = -20 + 100 Reorder the terms: -100 + 100 + -10a + 10b = -20 + 100 Combine like terms: -100 + 100 = 0 0 + -10a + 10b = -20 + 100 -10a + 10b = -20 + 100 Combine like terms: -20 + 100 = 80 -10a + 10b = 80 Add '-10b' to each side of the equation. -10a + 10b + -10b = 80 + -10b Combine like terms: 10b + -10b = 0 -10a + 0 = 80 + -10b -10a = 80 + -10b Divide each side by '-10'. a = -8 + b Simplifying a = -8 + b
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