https://file.aiquickdraw.com/mathbot/file/172631553784578a2q7k6.jpg

The given expression to factor is:

\[ 4p^3q - 6pq^2 \]

### Step-by-step factorization:

1. **Find the Greatest Common Factor (GCF):**
   - The GCF of the coefficients 4 and 6 is 2.
   - For the variables:
     - \( p^3 \) and \( p \) share \( p \).
     - \( q \) and \( q^2 \) share \( q \).

   So, the GCF is \( 2pq \).

2. **Factor out the GCF:**
   \[
   4p^3q - 6pq^2 = 2pq(2p^2 - 3q)
   \]

Thus, the completely factored form of the expression is:
\[
\boxed{2pq(2p^2 - 3q)}
\]

Would you like more details or have any questions on this?

---

Here are 5 related questions to expand on this topic:

1. How would you factor an expression like \( 5x^4y - 10x^2y^3 \)?
2. What are the steps to factor the difference of squares?
3. How can you factor a quadratic expression completely?
4. What is the role of prime factorization in finding the GCF of terms?
5. How do you check if a factorization is correct?

**Tip:** Always start by identifying the greatest common factor (GCF) to simplify expressions quickly!

Learn how to factorise the algebraic expression 4p^3q - 6pq^2 completely by finding the greatest common factor (GCF). This step-by-step solution is suitable for students in Grades 8-10, covering core algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation