Your friend asks you to check their work. You see the expression 3(15−9)2 + 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:
In Step 4, your friend's error was in multiplying 110 by 5 instead of adding 110 to 2 times 5. The correct operation should have been addition (+) instead of multiplication (⋅).
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 + 10
Step 4: 118
Part A: The error in your friend's work is in Step 4. They incorrectly multiplied 110 by 5 instead of adding 110 and 2 times 5 first.
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. Instead of multiplying 110 with 5, they should have added 110 to 2 multiplied by 5.
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 + 10
Step 4: 118