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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