In algebra, an equality that is true regardless of the numerical values assigned to its variables.
Symbol
The symbol “≡” is sometimes used for trigonometric identities.
Properties
These are special algebraic identities :
- \({(a+b)^2}\) = \({a^2}\)+ 2ab + \({b^2}\)
- \({(a–b)^2}\) = \({a^2}\)– 2ab + \({b^2}\)
- \({(a–b)^3}\) = \({a^3}\)– 3a\({b^2}\)+ 3\({a^2}\)b – \({b^3}\)
- \({(a+b)^3}\) = \({a^3}\)+ 3a\({b^2}\)+ 3\({a^2}\)b + \({b^3}\)
- \({a^2}\) – \({b^2}\) = (a + b) (a – b)
- \({a^3}\) – \({b^3}\) = (a – b)(\({a^2}\) + ab + \({b^2}\))
- \({a^3}\) + \({b^3}\) = (a + b)(\({a^2}\) – ab + \({b^2}\))
Examples
- The equality (a + b)² = a² + 2ab + b² is an algebraic identity.
- The relation sin (A + B) ≡ sin A cos B + sin B cos A is a trigonometric identity.