Algebraic Identities

Algebraic identities are equalities involving variables that hold for all values of those variables. They are used to expand, simplify, or factor algebraic expressions.

Important properties

• Identities are always true, unlike equations which may be true only for some values.

• They can be used to factorise or expand polynomials.

• Common identities include:

  • $(a + b)^2 = a^2 + 2ab + b^2$
  • $(a - b)^2 = a^2 - 2ab + b^2$
  • $a^2 - b^2 = (a - b)(a + b)$
  • $(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$
  • $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$
  • $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$
  • $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$