What is a3 + b3 Formula?

a³ + b³ formula is the basic algebra formula that gives the sum of two cubes without actually calculating the cubes.

Suppose we want to solve 12³ + 8³ without actually finding 12³ and 8³ then we use the a³ + b³ formula to find 12³ + 8³, without calculating the cubes of 8 and 12. The a³ + b³ formula is used to solve and simplify algebraic problems, it is also helpful in solving trigonometric problems, and others. The a³ + b³ formula is given in the image added as,

a³ + b³ Definition

a3 + b3 is a formula that is used to factorize a3 + b3 or it is used to find the sum of cubes of two numbers without actually calculating the cubes. It is derived from the expansion of (a + b)3 and is given as,

(a + b)³ = a³ + b³ + 3ab(a + b)

⇒ a³ + b³ = (a + b)³ – 3ab(a + b)

⇒ a³ + b³ = (a + b){(a + b)² – 3ab}

⇒ a³ + b³ = (a + b){a² + b² + 2ab – 3ab}

⇒ a³ + b³ = (a + b)(a² + b² – ab)

Factor of a³ + b³

To find the factor of a³ + b³ we use, the a³ + b³ formula added above, i.e. a³ + b³ = (a + b)(a² + b² -ab). This formula also gives the factor of a³ + b³. Factors of any number or polynomial are numbers or polynomials that on multiplying give the following number or polynomial. So by observing the a³ + b³ formula we can say that factors of a³ + b³ are,

Factors of a³ + b³ = (a + b)(a² – ab + b²)

a³ + b³ formula which is also called the sum of cubes formula, in algebra is the fundamental algebra formula that is used to find the sum of cubes of any two numbers without actually calculating their cubes. a³ + b³ formula is also used to find the factors of a³ + b³. This helps to simplify various algebraic expressions.

In this article, we will learn about, the a³ + b³ formula, factors of a³ + b³, examples, and others in detail.