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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 $5(5x+3y)(5x-3y)$.