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Factorize the expression $144a^2-289b^2$.
The given algebraic expression is $144a^2-289b^2$.
We have to factorize the expression $144a^2-289b^2$.
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.
Hence, the given expression can be factorized as $(12a+17b)(12a-17b)$.
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