Identify the property that justifies each step asked about in the answer area below.
Line 1: , left parenthesis, x, plus, 1, right parenthesis, left parenthesis, 10, plus, 9, x, right parenthesis
Line 1: =
(x+1)(10+9x)
Line 2: , left parenthesis, x, plus, 1, right parenthesis, left parenthesis, 9, x, plus, 10, right parenthesis
Line 2: =
(x+1)(9x+10)
Line 3: , left parenthesis, 9, x, plus, 10, right parenthesis, left parenthesis, x, plus, 1, right parenthesis
Line 3: =
(9x+10)(x+1)

The problem appears to involve identifying the mathematical properties used to justify each step of rewriting algebraic expressions. Let's analyze each line step by step:

### Line 1 to Line 2:
**Original Expression:**
\[
(x+1)(10+9x)
\]

**Rewritten as:**
\[
(x+1)(9x+10)
\]

**Justification:**  
This step involves **commutative property of addition**, which allows us to rewrite \(10 + 9x\) as \(9x + 10\). The commutative property states that for any two numbers, \(a + b = b + a\).

---

### Line 2 to Line 3:
**Original Expression:**
\[
(x+1)(9x+10)
\]

**Rewritten as:**
\[
(9x+10)(x+1)
\]

**Justification:**  
This step uses the **commutative property of multiplication**, which allows us to swap the order of the factors. The commutative property of multiplication states that \(a \cdot b = b \cdot a\), so \((x+1)(9x+10)\) can be rewritten as \((9x+10)(x+1)\).

---

### Summary:
- **Line 1 to Line 2:** Commutative Property of Addition.
- **Line 2 to Line 3:** Commutative Property of Multiplication.

Would you like further clarification or details on these properties? 

Here are some related questions you might find helpful:
1. What is the difference between the commutative properties of addition and multiplication?
2. Can the commutative property be applied to subtraction or division?
3. How does the associative property differ from the commutative property?
4. When is the commutative property most useful in algebra?
5. How would you simplify an expression like \((3x+2)(4x-5)\)?

**Tip:** The commutative property of multiplication is a powerful tool, especially when factoring or simplifying polynomial expressions.

Identify the property that justifies each step asked about in the answer area below. Line 1: (x+1)(10+9x) Line 2: (x+1)(9x+10) Line 3: (9x+10)(x+1)

Explore how to justify algebraic steps using the commutative properties of addition and multiplication. This problem involves rewriting expressions like (x+1)(10+9x) to (9x+10)(x+1), demonstrating core algebra concepts. Suitable for students in Grades 6-8.

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