What is the Formula of a3+b3?

By K Balaji|Updated : November 12th, 2022

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

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.

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