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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 $(lm-n^2)(m-1)$.