a3 plus b3 Formula

What is a3 +b3

The a3 +b3 formula is an algebraic identity which is read as a cube plus b cube. The a3 +b3 formula is used to find factorise cubes of binomials. 

a3+b3 Formula

Basic:

The a3 +b3 formula is an algebraic identity which is read as a cube plus b cube. The a3 +b3 formula is used to find factorise cubes of binomials. Thea3 +b3 formula helps us find the sum of cubes of two numbers easily without calculating the cubes of numbers. The a3 +b3 formula is applicable for all values of a and b. Sometime it is also called as ‘the sum of cubes’ formula.

We will be discussing aspects on the a3 +b3 formula, along with solved examples, and understand the identity involved.

What Is a3 +b3 Formula?

The a3 +b3 = (a+b)(a2-ab+b2) which can verified as well as can be derived from the formula (a+b)3. Lets discuss both aspects.

To verify a3+b3 = (a+b)(a2-ab+b2)

Solving the RHS

(a +b) (a2 - ab + b2)

Using binomial multiply with trinomial

= a (a2 -ab + b2)+b(a2 - ab + b2)

=a3- a2b + ab2+a2b-ab2+b3

=a3 + a2b-a2b + ab2-ab2+b3

=a3-0-0+b3

=a3+b3

LHS we have a3+b3

Therefore, LHS=RHS.

To prove by using (a+b)3 identity

Solved Example for a3 +b3 formula

Find the value of 103 + 23 by using the a3+b3 formula.

Solution: To find: 103 + 23.
Let us assume that a = 10 and b = 2
We will substitute these in the formula of a3 + b3 i.e., 
a3 + b3 = (a + b) (a2 - ab + b2)
103+23 = (100+8) = 108

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Frequently Asked Questions

The a3 + b3 Formula in Algebra is widely used in questions and it is applied in lots of explanations. this can be defined as 

 a3 + b3 = (a + b) (a2 - ab + b2)