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Simplifying (a + b)(c + d) = (c + d)(b + a) Multiply (a + b) * (c + d) (a(c + d) + b(c + d)) = (c + d)(b + a) ((c * a + d * a) + b(c + d)) = (c + d)(b + a) ((ac + ad) + b(c + d)) = (c + d)(b + a) (ac + ad + (c * b + d * b)) = (c + d)(b + a) (ac + ad + (bc + bd)) = (c + d)(b + a) (ac + ad + bc + bd) = (c + d)(b + a) Reorder the terms: ac + ad + bc + bd = (c + d)(a + b) Multiply (c + d) * (a + b) ac + ad + bc + bd = (c(a + b) + d(a + b)) ac + ad + bc + bd = ((a * c + b * c) + d(a + b)) ac + ad + bc + bd = ((ac + bc) + d(a + b)) ac + ad + bc + bd = (ac + bc + (a * d + b * d)) ac + ad + bc + bd = (ac + bc + (ad + bd)) Reorder the terms: ac + ad + bc + bd = (ac + ad + bc + bd) ac + ad + bc + bd = (ac + ad + bc + bd) Add '-1ac' to each side of the equation. ac + ad + bc + -1ac + bd = ac + ad + bc + -1ac + bd Reorder the terms: ac + -1ac + ad + bc + bd = ac + ad + bc + -1ac + bd Combine like terms: ac + -1ac = 0 0 + ad + bc + bd = ac + ad + bc + -1ac + bd ad + bc + bd = ac + ad + bc + -1ac + bd Reorder the terms: ad + bc + bd = ac + -1ac + ad + bc + bd Combine like terms: ac + -1ac = 0 ad + bc + bd = 0 + ad + bc + bd ad + bc + bd = ad + bc + bd Add '-1ad' to each side of the equation. ad + bc + -1ad + bd = ad + bc + -1ad + bd Reorder the terms: ad + -1ad + bc + bd = ad + bc + -1ad + bd Combine like terms: ad + -1ad = 0 0 + bc + bd = ad + bc + -1ad + bd bc + bd = ad + bc + -1ad + bd Reorder the terms: bc + bd = ad + -1ad + bc + bd Combine like terms: ad + -1ad = 0 bc + bd = 0 + bc + bd bc + bd = bc + bd Add '-1bc' to each side of the equation. bc + -1bc + bd = bc + -1bc + bd Combine like terms: bc + -1bc = 0 0 + bd = bc + -1bc + bd bd = bc + -1bc + bd Combine like terms: bc + -1bc = 0 bd = 0 + bd bd = bd Add '-1bd' to each side of the equation. bd + -1bd = bd + -1bd Combine like terms: bd + -1bd = 0 0 = bd + -1bd Combine like terms: bd + -1bd = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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