Factorize the expression $3x^3y-243xy^3$.

Given:

The given algebraic expression is $3x^3y-243xy^3$.

To do:

We have to factorize the expression $3x^3y-243xy^3$.

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.

$3x^3y-243xy^3$ 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. 

Therefore,

$3x^3y-243xy^3=3xy[(x)^2-(9y)^2]$

$3x^3y-243xy^3=3xy(x+9y)(x-9y)$

Hence, the given expression can be factorized as $3xy(x+9y)(x-9y)$.

Akhileshwar Nani

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Updated on: 08-Apr-2023

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