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Factorize the expression $ax+ay-bx-by$.
Given:
The given algebraic expression is $ax+ay-bx-by$.
To do:
We have to factorize the expression $ax+ay-bx-by$.
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 $ax+ay-bx-by$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $ax, ay, -bx$ and $-by$.
We can group the given terms as $ax, ay$ and $-bx, -by$.
Therefore, by taking $a$ as common in $ax, ay$ and $-b$ as common in $-bx, -by$, we get,
$ax+ay-bx-by=a(x+y)-b(x+y)$
Now, taking $(x+y)$ common, we get,
$ax+ay-bx-by=(x+y)(a-b)$
Hence, the given expression can be factorized as $(x+y)(a-b)$.
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