Identities are equations that are true for all values of the variables involved.This lesson is meant to summarize the various identities that are used in relation to polynomials:
| Identity | Expression |
| Binomial Theorem | \[(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k \] |
| Sum of Squares | \((a+b)^2 = a^2 + 2ab + b^2\) \( (a-b)^2 = a^2 - 2ab +b^2 \) |
| Difference of Squares | \(a^2 - b^2 = (a+b)(a-b)\) |
| Sum of Cubes | \( a^3 + b^3 =(a+b)(a^2 - ab + b^2) \) |
| Difference of Cubes | \( a^3 - b^3 =(a-b)(a^2 + ab +b^2) \) |