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Mastering Factoring Identities: Key Algebraic Formulas

Factoring Identities

These identities form the backbone of algebraic manipulation. Mastering them speeds up solving equations and simplifies expressions.

  1. Difference of Squares: a2 – b2 = (a + b)(a – b)

  2. Perfect Square (Sum): a2 + 2ab + b2 = (a + b)2

  3. Perfect Square (Difference): a2 – 2ab + b2 = (a – b)2

  4. Sum of Cubes: a3 + b3 = (a + b)(a2 – ab + b2)

  5. Difference of Cubes: a3 – b3 = (a – b)(a2 + ab + b2)

  6. Binomial Expansion – (a + b)3: a3 + 3a2b + 3ab2 + b3

  7. Binomial Expansion – (a – b)3: a3 – 3a2b + 3ab2 – b3

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