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Let's go through each part of this problem step-by-step.

### **Given Expression**:
The original expression is:
\[
18x^3 + 36x^5
\]

We need to factor out a common factor in each student's version and determine if they did it correctly. Let’s look at each student’s attempt.

---

### **Part A: Did Student A rewrite the expression correctly?**
**Student A’s version**:
\[
4x^3(4 + 9x^2)
\]
#### Steps:
- Start with \(18x^3 + 36x^5\).
- Find the greatest common factor (GCF) of the coefficients \(18\) and \(36\), which is **18**.
- Find the lowest power of \(x\), which is \(x^3\). So, the GCF of the expression is:
  \[
  18x^3
  \]

- Now divide each term by \(4x^3\), as Student A suggests:
  \[
  \frac{18x^3}{4x^3} = 4, \quad \frac{36x^ttaxest

Three students were asked to rewrite the expression 18x^3 + 36x^5 using a common factor. Did each student rewrite the expression correctly, and rewrite it using a different common factor than shown?

Explore how to factor algebraic expressions using a common factor, including checking student solutions for the expression 18x^3 + 36x^5. This example covers factoring concepts and the distributive property, ideal for Grades 6-8.

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