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 $(6l+m+n)(6l-m-n)$.