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Factorize the expression $36l^2-(m+n)^2$.
Given:
The given algebraic expression is $36l^2-(m+n)^2$.
To do:
We have to factorize the expression $36l^2-(m+n)^2$.
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.
$36l^2-(m+n)^2$ can be written as,
$36l^2-(m+n)^2=(6l)^2-(m+n)^2$ [Since $36=6^2$]
Here, we can observe that the given expression is a difference of two squares. So, by using the formula $a^2-b^2=(a+b)(a-b)$, we can factorize the given expression.
Therefore,
$36l^2-(m+n)^2=[6l+(m+n)][6l-(m+n)]$
$36l^2-(m+n)^2=(6l+m+n)(6l-m-n)$
Hence, the given expression can be factorized as $(6l+m+n)(6l-m-n)$.
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