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Factorize the expression $ab-by-ay+y^2$.
Given:
The given expression is $ab-by-ay+y^2$.
To do:
We have to factorize the expression $ab-by-ay+y^2$.
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 $ab-by-ay+y^2$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $ab, -by, -ay$ and $y^2$.
We can group the given terms as $ab, -ay$ and $-by, y^2$.
Therefore, by taking $a$ as common in $ab, -ay$ and $-y$ as common in $-by, y^2$, we get,
$ab-by-ay+y^2=a(b-y)-y(b-y)$
Now, taking $(b-y)$ common, we get,
$ab-by-ay+y^2=(a-y)(b-y)$
Hence, the given expression can be factorized as $(a-y)(b-y)$.
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