Your friend asks you to check their work. You see the expression 3( 15 - 9)^2 + • 5 simplified in the following way:
Original problem: 3( 15 -9)^2 + 2 • 5
Step 1: 3 (6)^2 + 2 • 5
Step 2: 3 (36) + 2 • 5
Step 3: 108 + 2 • 5
Step 4: 110 • 5
Step 5: 550
Part A: Explain, using complete sentences, in which step and what specifically your friend’s error was.
Part B: Correctly simplify this expression using a similar format - showing work for each step like was done above. Full credit will only be given if work shows Step 1, Step 2, Step 3, etc, as seen above.
Part A:
The error in your friend's work appears in Step 4. They made a mistake when multiplying 110 and 5. Instead of multiplying, they should have added these two numbers together.
Part B:
Step 1: 3(15 - 9)^2 + 2 • 5
Step 2: 3(6)^2 + 2 • 5
Step 3: 3(36) + 2 • 5
Step 4: 108 + 2 • 5
Step 5: 108 + 10
Step 6: 118
Part A: Your friend's error occurred in Step 4. They mistakenly multiplied 110 by 5 instead of adding 110 and 5 together.
Part B:
Original problem: 3(15 - 9)^2 + 2 • 5
Step 1: 3(6)^2 + 2 • 5
Step 2: 3(36) + 2 • 5
Step 3: 108 + 2 • 5
Step 4: 108 + 10
Step 5: 118
Part A: Your friend made an error in Step 4. Specifically, they incorrectly multiplied 110 by 5 instead of adding 110 and 5 together.
Part B:
Original problem: 3(15-9)^2 + 2•5
Step 1: 3(6)^2 + 2•5
Explanation: The first step is to evaluate the expression inside the parentheses, which is 15-9. Subtracting 9 from 15 gives us 6.
Step 2: 3(36) + 2•5
Explanation: Next, we need to square the result from step 1, which is 6^2. Squaring 6 gives us 36.
Step 3: 108 + 2•5
Explanation: In this step, we multiply 3 by 36, which gives us 108. Then we multiply 2 by 5, which equals 10.
Step 4: 108 + 10
Explanation: Now, we add the results from step 3 together. 108 plus 10 equals 118.
Therefore, the correct simplified expression is 118.