# Factorize the algebraic expression $p^2q^2-6pqr+9r^2$.

Given:

The given expression is $p^2q^2-6pqr+9r^2$.

To do:

We have to factorize the algebraic expression $p^2q^2-6pqr+9r^2$.

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.

$p^2q^2-6pqr+9r^2$ can be written as,

$p^2q^2-6pqr+9r^2=(pq)^2-2(pq)(3r)+(3r)^2$             [Since $p^2q^2=(pq)^2, 9r^2=(3r)^2$ and $6pqr=2(9pq)(3r)$]

Here, we can observe that the given expression is of the form $m^2-2mn+n^2$. So, by using the formula $(m-n)^2=m^2-2mn+n^2$, we can factorize the given expression.

Here,

$m=pq$ and $n=3r$

Therefore,

$p^2q^2-6pqr+9r^2=(pq)^2-2(pq)(3r)+(3r)^2$

$p^2q^2-6pqr+9r^2=(pq-3r)^2$

$p^2q^2-6pqr+9r^2=(pq-3r)(pq-3r)$

Hence, the given expression can be factorized as $(pq-3r)(pq-3r)$.

Updated on: 09-Apr-2023

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