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
The simplified expression is incorrect. The error occurred in Step 4. The expression should not be multiplied by 5, but rather added to it.
Here's the correct simplification:
Step 4: 108 + 2 ⋅ 5 = 108 + 10 = 118
Therefore, the correct simplified expression is 118.
The expression was simplified correctly. The final result is indeed 550.
To check if your friend's work is correct, we need to go through each step and perform the calculations.
Step 1: 3(6)2 + 2 ⋅5
To simplify the parentheses first, we evaluate 15 - 9, which is equal to 6.
The expression becomes: 3(6)2 + 2 ⋅ 5
Step 2: 3(36) + 2 ⋅ 5
Next, we calculate 6 squared, which is 6 multiplied by itself: 6 × 6 = 36.
The expression becomes: 3(36) + 2 ⋅ 5
Step 3: 108 + 2 ⋅ 5
Now, we multiply 3 by 36, which equals 108.
The expression becomes: 108 + 2 ⋅ 5
Step 4: 108 + 2 × 5
Next, we multiply 2 by 5, giving us 10.
The expression becomes: 108 + 10
Step 5: 108 + 10
Finally, we add 108 and 10, which gives us 118.
The final result is 118.
Therefore, your friend's work is incorrect. The correct answer is 118, not 550.