When expanding or factoring expressions, what property is being used? * Associative Property Commutaive Property Distributive Property What is the GCF (greatest common factor) of 12,32, and 407 * 2 4 6 Factor the following expression: * \[ 12 f+32 g+40 h \] \( 4(3 f+8 g+10 h) \) \( 4(3+8+10) \) \( 4 f(3+8 g+10 h) \)

Let's address each of your questions one by one: --- ### 1. **When expanding or factoring expressions, what property is being used?** **Answer:** **Distributive Property** **Explanation:** - The **Distributive Property** allows you to expand expressions like \( a(b + c) = ab + ac \) or factor expressions by factoring out the greatest common factor. - **Associative Property** relates to how terms are grouped in addition or multiplication (e.g., \( (a + b) + c = a + (b + c) \)). - **Commutative Property** pertains to the order of addition or multiplication (e.g., \( a + b = b + a \)). --- ### 2. **What is the GCF (greatest common factor) of 12, 32, and 407?** **Answer:** **1** **Explanation:** - **Prime Factorization:** - \( 12 = 2^2 \times 3 \) - \( 32 = 2^5 \) - \( 407 = 11 \times 37 \) - The only common factor among 12, 32, and 407 is **1**. **Note:** If the options provided (2, 4, 6) don't include 1, it might be worth double-checking the numbers or the options for a possible typo. --- ### 3. **Factor the following expression:** \[ 12f + 32g + 40h \] **Answer:** \( 4(3f + 8g + 10h) \) **Explanation:** - **Step 1:** Identify the Greatest Common Factor (GCF) of the coefficients 12, 32, and 40, which is **4**. - **Step 2:** Factor out the GCF: \[ 12f + 32g + 40h = 4(3f) + 4(8g) + 4(10h) = 4(3f + 8g + 10h) \] **Incorrect Options:** - \( 4(3 + 8 + 10) \) omits the variables. - \( 4f(3 + 8g + 10h) \) incorrectly factors out only \( f \) along with 4. --- If you have any further questions or need additional clarification, feel free to ask!