Question

solve the multi-step problem 6 - 4(3 - 1)^2 + 16

Answer 1

To solve the expression \(6 - 4(3 - 1)^2 + 16\), we will follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. **Evaluate the expression inside the parentheses**:
\[
3 - 1 = 2
\]

2. **Substitute back into the expression**:
\[
6 - 4(2)^2 + 16
\]

3. **Evaluate the exponent**:
\[
(2)^2 = 4
\]

4. **Substitute back into the expression**:
\[
6 - 4 \cdot 4 + 16
\]

5. **Perform the multiplication**:
\[
4 \cdot 4 = 16
\]

6. **Substitute back into the expression**:
\[
6 - 16 + 16
\]

7. **Perform the addition and subtraction from left to right**:
- First, calculate \(6 - 16\):
\[
6 - 16 = -10
\]
- Then, add \(16\):
\[
-10 + 16 = 6
\]

Thus, the final answer is:
\[
\boxed{6}
\]