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Factorize the expression $3x^3y-243xy^3$.
The given algebraic expression is $3x^3y-243xy^3$.
We have to factorize the expression $3x^3y-243xy^3$.
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.
$3x^3y-243xy^3$ can be written as,
$3x^3y-243xy^3=3xy(x^2-81y^2)$ (Taking $3xy$ common)
$3x^3y-243xy^3=3xy[(x)^2-(9y)^2]$ [Since $81=(9)^2$]
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 $3xy(x+9y)(x-9y)$.
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