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To factor the expression in part **b) 18a³ - 72ab²**, let's start by finding the greatest common factor (GCF) of the terms:

1. **Identify the GCF**: The GCF of \(18a^3\) and \(72ab^2\) is \(18a\).
   
2. **Factor out the GCF**: We divide each term by \(18a\):

   \[
   18a^3 \div 18a = a^2, \quad -72ab^2 \div 18a = -4b^2
   \]

   So, factoring out \(18a\), we have:

   \[
   18a(a^2 - 4b^2)
   \]

3. **Factor the remaining expression**: The expression \(a^2 - 4b^2\) is a difference of squares, which can be factored further as:

   \[
   a^2 - 4b^2 = (a - 2b)(a + 2b)
   \]

4. **Final factored form**: Substituting back, the complete factorization is:

   \[
   18a(a - 2b)(a + 2b)
   \]

Therefore, the factored form of **\(18a^3 - 72ab^2\)** is **\(18a(a - 2b)(a + 2b)\)**.

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

Here are some related questions you might find interesting:

1. How do you identify the greatest common factor in polynomial expressions?
2. What are the steps to factor a difference of squares?
3. How can you apply the distributive property to verify the factored expression?
4. What other methods can be used to factor trinomials or higher-degree polynomials?
5. Can you explain the relationship between factoring and solving polynomial equations?

**Tip:** Always check your factored form by expanding it back to ensure it matches the original expression.

Learn how to factor the polynomial 18a³ - 72ab² using the difference of squares method. This problem involves polynomials, factoring techniques, and the application of the difference of squares theorem. Suitable for students in Grades 9-12.

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