How can we put parentheses around the following expression so that the answer is 105?

9 + 8 x 7 - 6 x 5 + 4 x 3 + 2

[(9+8) x (7-6) x 5 ] + 4 x (3+2)

thanks

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To put parentheses around the expression so that the answer is 105, we need to determine the correct order of operations. The order of operations is as follows:

1. Parentheses (do operations within parentheses first)
2. Exponents (do any exponentiation)
3. Multiplication and Division (do these operations from left to right)
4. Addition and Subtraction (do these operations from left to right)

Let's look at the given expression step by step to determine where to place the parentheses.

9 + 8 × 7 - 6 × 5 + 4 × 3 + 2

First, we notice that there are multiplications and additions/subtractions in the expression. According to the order of operations, we should perform the multiplications before the additions and subtractions.

9 + (8 × 7) - (6 × 5) + (4 × 3) + 2

Now that we've enclosed the multiplications within parentheses, we can solve them first:

9 + (56) - (30) + (12) + 2

After solving the multiplications, we can proceed to the additions and subtractions:

9 + 56 - 30 + 12 + 2

Finally, we calculate the additions and subtractions from left to right:

77 - 30 + 12 + 2

47 + 12 + 2

59 + 2

61

By placing parentheses around the expression as shown above, the answer becomes 61. To obtain the answer of 105, there must be a different placement of parentheses in the expression.