# Factorize the expression $p^2q^2-p^4q^4$.

Given:

The given expression is $p^2q^2-p^4q^4$.

To do:

We have to factorize the expression $p^2q^2-p^4q^4$.

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.

$p^2q^2-p^4q^4$ can be written as,

$p^2q^2-p^4q^4=p^2q^2[1-p^2q^2]$               (Taking $p^2q^2$ common)

$p^2q^2-p^4q^4=p^2q^2[1^2-(pq)^2]$             [Since $p^2q^2=(pq)^2$]

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,

$p^2q^2-p^4q^4=p^2q^2[1^2-(pq)^2]$

$p^2q^2-p^4q^4=p^2q^2(1+pq)(1-pq)$

Hence, the given expression can be factorized as $p^2q^2(1+pq)(1-pq)$.

Updated on: 08-Apr-2023

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