simplify the expression using order of operations 2(5^2-2(9+1))

Answer 1

To simplify the expression \( 2(5^2 - 2(9 + 1)) \), we will follow the order of operations, 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 innermost parentheses: \[ 9 + 1 = 10 \] So the expression becomes: \[ 2(5^2 - 2(10)) \]

2. Evaluate the exponent: \[ 5^2 = 25 \] Now the expression is: \[ 2(25 - 2(10)) \]

3. Evaluate the multiplication in the parentheses: \[ 2(10) = 20 \] Thus, the expression simplifies to: \[ 2(25 - 20) \]

4. Subtract within the parentheses: \[ 25 - 20 = 5 \] Now we have: \[ 2(5) \]

5. Finally, perform the multiplication: \[ 2 \times 5 = 10 \]

Thus, the simplified expression is: \[ \boxed{10} \]