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