https://file.aiquickdraw.com/mathbot/file/1725017965441zerzy0i4.jpg

The expression given is:

\[
4p^3q - 81pq^3
\]

To factorize this expression, we first look for the greatest common factor (GCF) in the terms.

1. **Identify the GCF of coefficients**: The coefficients are 4 and 81, which have a GCF of 1.
   
2. **Identify the GCF of the variables**:
   - Both terms have \( p \) and \( q \).
   - The lowest power of \( p \) is \( p \), and the lowest power of \( q \) is \( q \).

Thus, the GCF of the expression is \( pq \).

3. **Factor out the GCF**:

\[
4p^3q - 81pq^3 = pq(4p^2 - 81q^2)
\]

4. **Further factorization**: Notice that \( 4p^2 - 81q^2 \) is a difference of squares, which can be factored further:

\[
4p^2 - 81q^2 = (2p - 9q)(2p + 9q)
\]

So the fully factorized expression is:

\[
pq(2p - 9q)(2p + 9q)
\]

Would you like any further details or have any questions?

Here are five related questions you might find helpful:

1. How can you recognize a difference of squares in an expression?
2. What other types of factoring techniques are commonly used?
3. How do you factor trinomials that are not perfect squares?
4. What is the importance of identifying the GCF before factoring?
5. Can the difference of cubes be factored similarly to the difference of squares?

**Tip:** Always check if a quadratic expression can be factored further by looking for common patterns like the difference of squares or perfect square trinomials.

Learn how to factorize the expression 4p^3q - 81pq^3 step-by-step. Understand the concept of factoring polynomials and recognizing the difference of squares pattern. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation