Factorize the expression $125x^2-45y^2$.

Given:

The given algebraic expression is $125x^2-45y^2$.

To do:

We have to factorize the expression $125x^2-45y^2$.

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.

$125x^2-45y^2$ can be written as,

$125x^2-45y^2=5[25x^2-9y^2]$                (Taking $5$ as common)

$125x^2-45y^2=5[(5x)^2-(3y)^2]$             [Since $25=5^2, 9=3^2$]

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,

$125x^2-45y^2=5[(5x)^2-(3y)^2]$

$125x^2-45y^2=5(5x+3y)(5x-3y)$

Hence, the given expression can be factorized as $5(5x+3y)(5x-3y)$.

Akhileshwar Nani

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Updated on: 07-Apr-2023

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