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Factorize the expression $x^2-11xy-x+11y$.
Given:
The given expression is $x^2-11xy-x+11y$.
To do:
We have to factorize the expression $x^2-11xy-x+11y$.
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 $x^2-11xy-x+11y$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $x^2, -11xy, -x$ and $11y$.
We can group the given terms as $x^2, -11xy$ and $-x, 11y$.
Therefore, by taking $x$ as common in $x^2, -11xy$ and $-1$ as common in $-x, 11y$, we get,
$x^2-11xy-x+11y=x(x-11y)-1(x-11y)$
Now, taking $(x-11y)$ common, we get,
$x^2-11xy-x+11y=(x-1)(x-11y)$
Hence, the given expression can be factorized as $(x-1)(x-11y)$.