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Simplifying a2 + 4b2 + 4ab + -1(a + 2b)(a + b) = 0 Multiply (a + 2b) * (a + b) a2 + 4b2 + 4ab + -1(a(a + b) + 2b * (a + b)) = 0 a2 + 4b2 + 4ab + -1((a * a + b * a) + 2b * (a + b)) = 0 Reorder the terms: a2 + 4b2 + 4ab + -1((ab + a2) + 2b * (a + b)) = 0 a2 + 4b2 + 4ab + -1((ab + a2) + 2b * (a + b)) = 0 a2 + 4b2 + 4ab + -1(ab + a2 + (a * 2b + b * 2b)) = 0 a2 + 4b2 + 4ab + -1(ab + a2 + (2ab + 2b2)) = 0 Reorder the terms: a2 + 4b2 + 4ab + -1(ab + 2ab + a2 + 2b2) = 0 Combine like terms: ab + 2ab = 3ab a2 + 4b2 + 4ab + -1(3ab + a2 + 2b2) = 0 a2 + 4b2 + 4ab + (3ab * -1 + a2 * -1 + 2b2 * -1) = 0 a2 + 4b2 + 4ab + (-3ab + -1a2 + -2b2) = 0 Reorder the terms: 4ab + -3ab + a2 + -1a2 + 4b2 + -2b2 = 0 Combine like terms: 4ab + -3ab = 1ab 1ab + a2 + -1a2 + 4b2 + -2b2 = 0 Combine like terms: a2 + -1a2 = 0 1ab + 0 + 4b2 + -2b2 = 0 1ab + 4b2 + -2b2 = 0 Combine like terms: 4b2 + -2b2 = 2b2 1ab + 2b2 = 0 Solving 1ab + 2b2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b2' to each side of the equation. 1ab + 2b2 + -2b2 = 0 + -2b2 Combine like terms: 2b2 + -2b2 = 0 1ab + 0 = 0 + -2b2 1ab = 0 + -2b2 Remove the zero: 1ab = -2b2 Divide each side by '1b'. a = -2b Simplifying a = -2b
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