Factorize the expression $ab-a-b+1$.

Given:

The given algebraic expression is $ab-a-b+1$.

To do:

We have to factorize the expression $ab-a-b+1$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression implies 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 factorize the expression $ab-a-b+1$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $ab, -a, -b$ and $1$.

We can group the given terms as $ab, -a$ and $-b, 1$. 

Therefore, by taking $a$ as common in $ab, -a$ and $-1$ as common in $-b, 1$, we get,

$ab-a-b+1=a(b-1)-1(b-1)$

Now, taking $(b-1)$ common, we get,

$ab-a-b+1=(a-1)(b-1)$

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

Akhileshwar Nani

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Updated on: 06-Apr-2023

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