Factorize the expression $x^2-2ax-2ab+bx$.

Given:

The given expression is $x^2-2ax-2ab+bx$.

To do:

We have to factorize the expression $x^2-2ax-2ab+bx$.

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 $x^2-2ax-2ab+bx$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $x^2, -2ax, -2ab$ and $bx$.

We can group the given terms as $x^2, bx$ and $-2ax, -2ab$. 

Therefore, by taking $x$ as common in $x^2, bx$ and $-2a$ as common in $-2ax, -2ab$, we get,

$x^2-2ax-2ab+bx=x(x+b)-2a(x+b)$

Now, taking $(x+b)$ common, we get,

$x^2-2ax-2ab+bx=(x+b)(x-2a)$

Hence, the given expression can be factorized as $(x+b)(x-2a)$.

Akhileshwar Nani

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Updated on: 06-Apr-2023

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