Simplify and evaluate each of the following expressions: a. \( (10 x \times 6.7 x)-(11 x \times 6 x) \), where \( x=30 \) Round to two decimal places b. \( (4 x)(13 x+0.25 x)(0.5 x+1 x) \), where \( x=3 \) Round to two decimal places

**a. Expression: \( (10x \times 6.7x) - (11x \times 6x) \) where \( x=30 \)** 1. **Simplify the expression:** Multiply the constants and combine the \( x \) terms: \[ (10x \times 6.7x) = 10 \times 6.7 \times x^2 = 67x^2 \] \[ (11x \times 6x) = 11 \times 6 \times x^2 = 66x^2 \] Thus, the expression becomes: \[ 67x^2 - 66x^2 = x^2 \] 2. **Substitute \( x = 30 \):** \[ x^2 = 30^2 = 900 \] 3. **Round to two decimal places:** \[ 900.00 \] --- **b. Expression: \( (4x)(13x+0.25x)(0.5x+1x) \) where \( x=3 \)** 1. **Simplify the expression:** First, simplify the factors inside the parentheses: \[ 13x + 0.25x = (13+0.25)x = 13.25x \] \[ 0.5x + 1x = (0.5+1)x = 1.5x \] The expression then becomes: \[ (4x)(13.25x)(1.5x) \] 2. **Combine the terms:** Multiply the constants and the \( x \) terms: \[ 4 \times 13.25 \times 1.5 = 79.5 \] and \[ x \times x \times x = x^3 \] So, the simplified expression is: \[ 79.5x^3 \] 3. **Substitute \( x = 3 \):** \[ 79.5 \times 3^3 = 79.5 \times 27 \] Compute the multiplication: \[ 79.5 \times 27 = 2146.5 \] 4. **Round to two decimal places:** \[ 2146.50 \] --- **Final Answers:** a. \(900.00\) b. \(2146.50\)