Factorize the expression $lm^2-mn^2-lm+n^2$.

Given:

The given expression is $lm^2-mn^2-lm+n^2$.

To do:

We have to factorize the expression $lm^2-mn^2-lm+n^2$.

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 factorize the expression $lm^2-mn^2-lm+n^2$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $lm^2, -mn^2, -lm$ and $n^2$.

We can group the given terms as $lm^2, -lm$ and $-mn^2, n^2$. 

Therefore, by taking $lm$ as common in $lm^2, -lm$ and $-n^2$ as common in $-mn^2, n^2$, we get,

$lm^2-mn^2-lm+n^2=lm(m-1)-n^2(m-1)$

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

$lm^2-mn^2-lm+n^2=(lm-n^2)(m-1)$

Hence, the given expression can be factorized as $(lm-n^2)(m-1)$.

Akhileshwar Nani

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Updated on: 06-Apr-2023

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