# Algebraic Identity

## Algebraic Identity

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) (ab)
• $${a^3}$$ –  $${b^3}$$ = (ab)($${a^2}$$ + 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.