Algebraic Identities

In literal calculus, there are some significant algebraic identities that could be used to quickly evaluate the product between polynomials without resorting to the complete procedure. They are called Algebraic Identities.

Another important use of these identities is to factorize polynomials as we will see in the next chapter.

On this page, we list the main such identities, providing links to the corresponding pages that show their detailed proof.

Significant Algebraic Identities

Below are the main algebraic identities. For a complete explanation, refer to the corresponding link.

Definition

Square of a Binomial

\Large (a + b)^2 \, = \, a^2 + 2ab + b^2
Definition

Square of a Trinomial

\Large (a + b + c)^2 \, = \, a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
Definition

Product of the sum of two monomials and their difference

\Large (a + b) \cdot (a - b) \, = \, a^2 - b^2
Definition

Cube of a Binomial

\Large (a + b)^3 \, = \, a^3 + 3a^2b + 3ab^2 + b^3
Definition

Power of a Binomial

\Large (a + b)^n
Definition

Difference of two Cubes

\Large (A^3 - B^3) \, = \, (A - B) \cdot (A^2 + AB + B^2)
Definition

Sum of two Cubes

\Large (A^3 + B^3) \, = \, (A + B) \cdot (A^2 - AB + B^2)