Source: Extra Practice

Simplify the expression: 5×[10−(8−2×(6−4))]5 \times [10 - (8 - 2 \times (6 - 4))].

Options

Option A

1010

Option B

2020

Option C is correct

3030

Option D

4040

Explanation

We simplify the expression by working from the innermost brackets outwards:

  1. Innermost parenthesis: (6−4)=2(6 - 4) = 2 The expression becomes: 5×[10−(8−2×2)]5 \times [10 - (8 - 2 \times 2)]
  2. Multiplication inside parenthesis: 2×2=42 \times 2 = 4 The expression becomes: 5×[10−(8−4)]5 \times [10 - (8 - 4)]
  3. Subtraction inside parenthesis: (8−4)=4(8 - 4) = 4 The expression becomes: 5×[10−4]5 \times [10 - 4]
  4. Subtraction inside square bracket: [10−4]=6[10 - 4] = 6 The expression becomes: 5×65 \times 6
  5. Final Multiplication: 5×6=305 \times 6 = 30 Thus, the simplified value is 3030. Other options result from errors in the order of operations, especially with brackets.