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 $(x-1)(x-11y)$.

Updated on: 06-Apr-2023

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