2. Solve the following in two different ways. \( \begin{array}{ll}\text { a. } 6(17+9)= \\ \begin{array}{ll}\text { c. } 7 \times(4-1)= & \text { (b. } 12(26-8)= \\ \text { e. } 42 \times 2) \times 5= & \text { f. }(12+13) \times 2= \\ \text { g. } 16(112-9)= & \text { (h. } 5-3(4+5)=\end{array}\end{array} \).

Sure! Let's solve each of the given expressions in **two different ways**. We'll use methods such as simplifying inside the parentheses first, distributing multiplication, and applying the associative property where applicable. --- ### **a. \(6(17 + 9)\)** **Method 1: Simplify Inside the Parentheses First** 1. **Add inside the parentheses:** \[ 17 + 9 = 26 \] 2. **Multiply by 6:** \[ 6 \times 26 = 156 \] **Answer:** \(156\) --- **Method 2: Use the Distributive Property** 1. **Distribute the multiplication over addition:** \[ 6 \times 17 + 6 \times 9 = 102 + 54 \] 2. **Add the results:** \[ 102 + 54 = 156 \] **Answer:** \(156\) --- ### **b. \(12(26 - 8)\)** **Method 1: Simplify Inside the Parentheses First** 1. **Subtract inside the parentheses:** \[ 26 - 8 = 18 \] 2. **Multiply by 12:** \[ 12 \times 18 = 216 \] **Answer:** \(216\) --- **Method 2: Use the Distributive Property** 1. **Distribute the multiplication over subtraction:** \[ 12 \times 26 - 12 \times 8 = 312 - 96 \] 2. **Subtract the results:** \[ 312 - 96 = 216 \] **Answer:** \(216\) --- ### **c. \(7 \times (4 - 1)\)** **Method 1: Simplify Inside the Parentheses First** 1. **Subtract inside the parentheses:** \[ 4 - 1 = 3 \] 2. **Multiply by 7:** \[ 7 \times 3 = 21 \] **Answer:** \(21\) --- **Method 2: Use the Distributive Property** 1. **Distribute the multiplication:** \[ 7 \times 4 - 7 \times 1 = 28 - 7 \] 2. **Subtract the results:** \[ 28 - 7 = 21 \] **Answer:** \(21\) --- ### **e. \((42 \times 2) \times 5\)** **Method 1: Perform Multiplications Sequentially** 1. **Multiply inside the first parentheses:** \[ 42 \times 2 = 84 \] 2. **Multiply the result by 5:** \[ 84 \times 5 = 420 \] **Answer:** \(420\) --- **Method 2: Use the Associative Property** 1. **Rearrange the multiplication without changing the result:** \[ 42 \times (2 \times 5) = 42 \times 10 \] 2. **Multiply:** \[ 42 \times 10 = 420 \] **Answer:** \(420\) --- ### **f. \((12 + 13) \times 2\)** **Method 1: Simplify Inside the Parentheses First** 1. **Add inside the parentheses:** \[ 12 + 13 = 25 \] 2. **Multiply by 2:** \[ 25 \times 2 = 50 \] **Answer:** \(50\) --- **Method 2: Use the Distributive Property** 1. **Distribute the multiplication over addition:** \[ 12 \times 2 + 13 \times 2 = 24 + 26 \] 2. **Add the results:** \[ 24 + 26 = 50 \] **Answer:** \(50\) --- ### **g. \(16(112 - 9)\)** **Method 1: Simplify Inside the Parentheses First** 1. **Subtract inside the parentheses:** \[ 112 - 9 = 103 \] 2. **Multiply by 16:** \[ 16 \times 103 = 1,\!648 \] **Answer:** \(1,\!648\) --- **Method 2: Break Down the Multiplication** 1. **Express 103 as 100 + 3:** \[ 16 \times (100 + 3) = 16 \times 100 + 16 \times 3 \] 2. **Multiply each part:** \[ 16 \times 100 = 1,\!600 \\ 16 \times 3 = 48 \] 3. **Add the results:** \[ 1,\!600 + 48 = 1,\!648 \] **Answer:** \(1,\!648\) --- ### **h. \(5 - 3(4 + 5)\)** **Method 1: Simplify Inside the Parentheses First** 1. **Add inside the parentheses:** \[ 4 + 5 = 9 \] 2. **Multiply by 3:** \[ 3 \times 9 = 27 \] 3. **Subtract from 5:** \[ 5 - 27 = -22 \] **Answer:** \(-22\) --- **Method 2: Use the Distributive Property** 1. **Distribute the multiplication:** \[ 5 - 3 \times 4 - 3 \times 5 = 5 - 12 - 15 \] 2. **Subtract sequentially:** \[ 5 - 12 = -7 \\ -7 - 15 = -22 \] **Answer:** \(-22\) --- By applying different mathematical properties and methods, we consistently arrive at the same correct answers for each expression.