Factorize the expression $144a^2-289b^2$.

Given:

The given algebraic expression is $144a^2-289b^2$.

To do:

We have to factorize the expression $144a^2-289b^2$.

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.

$144a^2-289b^2$ can be written as,

$144a^2-289b^2=(12a)^2-(17b)^2]$             [Since $144=(12)^2, 289=(17)^2$]

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,

$144a^2-289b^2=(12a)^2-(17b)^2$

$144a^2-289b^2=(12a+17b)(12a-17b)$

Hence, the given expression can be factorized as $(12a+17b)(12a-17b)$.