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Factorize the expression $p^2q-pr^2-pq+r^2$.
Given:
The given algebraic expression is $p^2q-pr^2-pq+r^2$.
To do:
We have to factorize the expression $p^2q-pr^2-pq+r^2$.
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 $p^2q-pr^2-pq+r^2$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $p^2q, -pr^2, -pq$ and $r^2$.
We can group the given terms as $p^2q, -pq$ and $-pr^2, r^2$.
Therefore, by taking $pq$ as common in $p^2q, -pq$ and $r^2$ as common in $-pr^2, r^2$, we get,
$p^2q-pr^2-pq+r^2=pq(p-1)+r^2(-p+1)$
$r^2(-p+1)$ can be written as,
$r^2(-p+1)=-r^2(p-1)$
Therefore,
$p^2q-pr^2-pq+r^2=pq(p-1)-r^2(p-1)$
Now, taking $(p-1)$ common, we get,
$p^2q-pr^2-pq+r^2=(p-1)(pq-r^2)$
Hence, the given expression can be factorized as $(p-1)(pq-r^2)$.
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