Certainly! Let's factor the given expression step-by-step.
The expression is:
[tex]\[ 81p^2 - 4pq^2 \][/tex]
To factorize this expression, we will look for common factors and special algebraic identities.
1. Identify Common Factors:
Observe if there is a common factor in the terms of the expression. In this case, the expression does not have a straightforward common factor other than [tex]\( p \)[/tex].
2. Rewrite the Expression:
Let's factor out [tex]\( p \)[/tex] from each term:
[tex]\[
81p^2 - 4pq^2 = p(81p - 4q^2)
\][/tex]
3. Verify the Factorization:
To ensure our factorization is correct, we can distribute [tex]\( p \)[/tex] back into the terms inside the parentheses:
[tex]\[
p(81p - 4q^2) \implies 81p^2 - 4pq^2
\][/tex]
Therefore, the factorized form of the expression [tex]\( 81p^2 - 4pq^2 \)[/tex] is:
[tex]\[ p(81p - 4q^2) \][/tex]
This is the expression expressed as a product of two terms.
