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