What is the Formula of (a - b)3 ?

By Esha Dhawan|Updated : August 10th, 2022

Candidates preparing for any government exam must be aware of algebraic formulas to score the maximum marks in the Quantitative Aptitude section. Knowing the basic algebraic formulas like (a - b)3 can help you sail through the exam smoothly. To calculate the formula of (a - b)3, candidates need to just multiply (a - b)(a - b)(a - b). This algebraic formula is derived to find the cube of a binomial.


Formula of (a - b)3 is a3 - 3ab(a-b) - b3

Let us check the derivation of (a - b)3 formula:

(a - b)3 can be simply written as (a - b)(a - b)(a - b)

Which can further be written as (a - b)2 (a - b)

You must be aware of the formula for (a - b)2  which says (a - b)2 = (a2 - 2ab + b2)

So, (a2 - 2ab + b2) can be written as following

 = (a2 - 2ab + b2)(a - b)

Opening the brackets and multiplying with the terms we get following

 = a3 - a2b - 2a2b + 2ab2 + ab2 - b3

Simplifying further we get the following expression

 = a3 - 3a2b + 3ab2 - b3

Take out the common term (-3ab), we get following

 = a3 - 3ab(a-b) - b3

Hence proved, (a - b)3 = a3 - 3ab(a-b) - b3


What is the Formula of (a - b)3 ?

The (a - b)3 Formula is used to calculate the difference between a & b. This algebraic identity is used to find the cube of a binomial.


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