Alternative Decompositions of the Difference of Two Squares

This note presents two alternative algebraic decompositions of the difference of two squares. The identities are algebraically equivalent to the standard factorization a² − b² = (a+b)(a−b), but express the same quantity using either (a−b) or (a+b) as a central quantity. According to the author's recollection, these forms were independently derived in 2017 while the author was a Grade 10 student, without consulting books, teachers, or online sources. Difference of squaresAlgebraic identitiesAlgebraAlternative algebraic formsIndependent derivationMathematical identity