What is the Formula of (a – b)3 ?

Answer:

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

Summary:

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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