Factorize the expression $abx^2+(ay-b)x-y$.


The given expression is $abx^2+(ay-b)x-y$.

To do:

We have to factorize the expression $abx^2+(ay-b)x-y$.


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 $abx^2+(ay-b)x-y$ by grouping similar terms and taking out the common factors.

We can write $abx^2+(ay-b)x-y$ as,


The terms in the given expression are $abx^2, ayx, -bx$ and $-y$.

We can group the given terms as $abx^2, -bx$ and $axy, -y$

Therefore, by taking $bx$ as common in $abx^2, -bx$ and $y$ as common in $axy, -y$, we get,


Now, taking $(ax-1)$ common, we get,


Hence, the given expression can be factorized as $(bx+y)(ax-1)$.

Updated on: 06-Apr-2023


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