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Factorize the expression $6xy+6-9y-4x$.
Given:
The given algebraic expression is $6xy+6-9y-4x$.
To do:
We have to factorize the expression $6xy+6-9y-4x$.
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 $6xy+6-9y-4x$ by grouping similar terms and taking out the common factors.
The terms in the given expression are $6xy, 6, -9y$ and $-4x$.
We can group the given terms as $6xy, -4x$ and $6, -9y$.
Therefore, by taking $2x$ as common in $6xy, -4x$ and $-3$ as common in $6, -9y$, we get,
$6xy+6-9y-4x=2x(3y-2)-3(-2+3y)$
$6xy+6-9y-4x=2x(3y-2)-3(3y-2)$
Now, taking $(3y-2)$ common, we get,
$6xy+6-9y-4x=(3y-2)(2x-3)$
Hence, the given expression can be factorized as $(3y-2)(2x-3)$.
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