Simplify $(2+3)^2-16 \div 2$.
Answer (1)
To simplify the expression ( 2 + 3 ) 2 − 16 ÷ 2 :
Evaluate the parentheses: 2 + 3 = 5 .
Evaluate the exponent: 5 2 = 25 .
Perform the division: 16 ÷ 2 = 8 .
Subtract: 25 − 8 = 17 .
The final answer is 17 .
Explanation
Understanding the Expression We are asked to simplify the expression ( 2 + 3 ) 2 − 16 ÷ 2 . To do this, we will follow the order of operations (PEMDAS/BODMAS).
Parentheses First, we evaluate the expression inside the parentheses: 2 + 3 = 5
Exponents Next, we evaluate the exponent: 5 2 = 5 × 5 = 25
Division Now, we perform the division: 16 ÷ 2 = 8
Subtraction Finally, we perform the subtraction: 25 − 8 = 17
Final Answer Therefore, the simplified expression is 17.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating expenses or determining the outcome of a scientific experiment. For example, if you are calculating the total cost of items with discounts and taxes, you need to apply the operations in the correct order to get the accurate final cost. Similarly, in physics, correctly applying the order of operations ensures accurate calculations of forces and energies.
