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Factorize the expression $abx^2+(ay-b)x-y$.
Given:
The given expression is $abx^2+(ay-b)x-y$.
To do:
We have to factorize the expression $abx^2+(ay-b)x-y$.
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 $abx^2+(ay-b)x-y$ by grouping similar terms and taking out the common factors.
We can write $abx^2+(ay-b)x-y$ as,
$abx^2+(ay-b)x-y=abx^2+axy-bx-y$
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,
$abx^2+(ay-b)x-y=bx(ax-1)+y(ax-1)$
Now, taking $(ax-1)$ common, we get,
$abx^2+(ay-b)x-y=(bx+y)(ax-1)$
Hence, the given expression can be factorized as $(bx+y)(ax-1)$.
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