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