What is the Formula of a3+b3?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The formula of a³+b³ is a³+b³=a+ba²+b²-ab.

Formula of a³+b³

Now we have to find the formula for a³+b³.

Considering that for each real number, a and b

(a+b)³=a³+b³+3ab(a+b)…(1)

From the equation(1), the value a³+b³ is derived as follows:

a³+b³=(a+b)³-3ab(a+b)

⇒a³+b³=a+ba+b²-3ab…(2)

Substitute the value of a+b² from (a+b)²=a²+b²+2ab in (2):

a³+b³=a+ba²+b²+2ab-3ab⇒a³+b³=a+ba²+b²-ab

Table of content

1. What is the Formula of a3+b3?

Algebraic identities are equations in algebra that are true regardless of the value of each of their variables. Mathematical equations with numbers, variables (unknown values), and mathematical operators are known as algebraic identities and expressions (addition, subtraction, multiplication, division, etc.)

Numerous areas of mathematics, including algebra, geometry, trigonometry, etc., use algebraic identities. These are mostly employed to identify the polynomials’ factors. A deeper comprehension of algebraic identities helps to improve one’s ability to answer sum problems quickly. The factorization of polynomials is one of the most significant uses for algebraic identities.

Hence, the formula for a³+b³ is a³+b³=a+ba²+b²-ab.

Summary:-

What is the Formula of a³+b³?

The formula of a³+b³ is a³+b³=a+ba²+b²-ab. An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value.

Related Questions:-

What is the Formula of a3+b3?

Formula of a3+b3