Factorize the expression $a^2-b^2+a-b$.

Given:

The given expression is $a^2-b^2+a-b$.

To do:

We have to factorize the expression $a^2-b^2+a-b$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression means writing the expression as a product of two or more factors. Factorization is the reverse of distribution. 

An algebraic expression is factored completely when it is written as a product of prime factors.

Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression. 

Therefore,

$a^2-b^2+a-b=(a+b)(a-b)+a-b$

$a^2-b^2+a-b=(a-b)[(a+b)+1]$                                (Taking $(a-b)$ common)

$a^2-b^2+a-b=(a-b)(a+b+1)$

Hence, the given expression can be factorized as $(a-b)(a+b+1)$.

Akhileshwar Nani

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Updated on: 09-Apr-2023

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