$(3+1)^2-17
cdot 2+24+3+5
Answer (2)
To evaluate the expression ( 3 + 1 ) 2 − 17 ⋅ 2 + 24 + 3 + 5 , we simplify it step-by-step using the order of operations, resulting in the final answer of 14. The steps include simplifying parentheses, evaluating exponents, performing multiplication, and solving the addition and subtraction. Thus, the final result is 14 .
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Simplify inside the parentheses: ( 3 + 1 ) = 4 .
Evaluate the exponent: 4 2 = 16 .
Perform the multiplication: 17 ⋅ 2 = 34 .
Perform addition and subtraction from left to right: 16 − 34 + 24 + 3 + 5 = 14 .
The final answer is 14 .
Explanation
Understanding the Problem We are asked to simplify the expression ( 3 + 1 ) 2 − 17"."2 + 24 + 3 + 5 following the order of operations (PEMDAS/BODMAS). This means we need to handle parentheses first, then exponents, then multiplication and division, and finally addition and subtraction from left to right.
Simplifying Parentheses First, we simplify the expression inside the parentheses: ( 3 + 1 ) = 4 .
Evaluating Exponents Next, we evaluate the exponent: 4 2 = 16 .
Performing Multiplication Now, we perform the multiplication: 17 ⋅ 2 = 34 .
Performing Addition and Subtraction Finally, we perform addition and subtraction from left to right: 16 − 34 + 24 + 3 + 5 . Let's break this down step by step:
16 − 34 = − 18
− 18 + 24 = 6
6 + 3 = 9
9 + 5 = 14
Final Answer Therefore, the simplified expression is equal to 14.
Examples
Order of operations is a crucial concept that applies to many real-life situations. For example, when calculating the total cost of items with discounts and taxes, you need to follow the correct order to get the right answer. Imagine you're buying a shirt that costs $25, has a 20% discount, and then a 6% sales tax is applied. You first calculate the discount amount ($25 * 0.20 = $5), subtract it from the original price ($25 - $5 = $20), and then calculate the sales tax ($20 * 0.06 = $1.20). Finally, you add the sales tax to the discounted price ($20 + $1.20 = $21.20). If you did not follow the correct order, you would end up with a different and incorrect final price.
