Factorize the expression $144a^2-169b^2$.

Given:

The given expression is $144a^2-169b^2$.

To do:

We have to factorize the expression $144a^2-169b^2$.

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.

$144a^2-169b^2$ can be written as,

$144a^2-169b^2=(12a)^2-(13b)^2]$             [Since $144=(12)^2, 169=(13)^2$]

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,

$144a^2-169b^2=(12a)^2-(13b)^2$

$144a^2-169b^2=(12a+13b)(12a-13b)$

Hence, the given expression can be factorized as $(12a+13b)(12a-13b)$.

Akhileshwar Nani

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Updated on: 07-Apr-2023

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