There isn't a finite number of algebraic identities, but some are more commonly used than others. Here are four basic and frequently used algebraic identities, as presented by Vedantu:
Four Basic Algebraic Identities
These identities are fundamental in algebra and are widely used for simplifying expressions and solving equations.
| Identity | Formula |
|---|---|
| Identity I | (a+b)2 = a2+2ab+b2 |
| Identity II | (a-b)2 = a2- 2ab+b2 |
| Identity III | a2-b2= (a+b) (a-b) |
| Identity IV | (x+a) (x+b) = x2+(a+b) x+ab |
Examples of Using the Identities:
-
Identity I: (a+b)2 = a2+2ab+b2
- Example: Expand (x + 3)2
- Solution: x2 + 2(x)(3) + 32 = x2 + 6x + 9
-
Identity II: (a-b)2 = a2- 2ab+b2
- Example: Expand (y - 2)2
- Solution: y2 - 2(y)(2) + 22 = y2 - 4y + 4
-
Identity III: a2-b2= (a+b) (a-b)
- Example: Factor x2 - 16
- Solution: (x + 4)(x - 4)
-
Identity IV: (x+a) (x+b) = x2+(a+b) x+ab
- Example: Expand (x + 2)(x + 5)
- Solution: x2 + (2+5)x + (2)(5) = x2 + 7x + 10
It is important to understand that these are not all the algebraic identities that exist. There are infinitely many, but these four are foundational and taught in early algebra education.
