Problem 31 - Algebra 1

Question

Evaluate the expression. $$\left[(7-4)^{2}+3\right]+15$$

Step-by-Step Solution

Answer

The evaluated result of the given expression is 27.

Step 1: Handle the Parentheses

According to the BODMAS rule, operations enclosed in Parentheses are done first. Hence, calculate the expression (7-4), which will evaluate to 3.

Step 2: Exponent Calculation

The next operation according to the order of operations rule is Exponents. Therefore, calculate the square of the result from the previous step, which is \(3^2\). This evaluates to 9.

Step 3: Handle the addition inside Parentheses

Now we'll add the result of the squared value to 3 (i.e. 9 + 3). This will evaluate to 12.

Step 4: Final Addition

Finally, add the result from the last step to 15. So, 12 + 15 = 27.

Key Concepts

BODMAS rule

The BODMAS rule is a mnemonic to help you remember the correct order of operations in mathematics. Each letter stands for a different operation:

• Brackets (or Parentheses)
• Orders (or Exponents)
• Division
• Multiplication
• Addition
• Subtraction

Following the BODMAS rule ensures that mathematical expressions are solved correctly and consistently. Start with operations inside Parentheses, then move to Exponents, and so on. This order prevents errors and confusion, especially in complex calculations. By adhering to this rule, you ensure clarity and accuracy in solving expressions.

Parentheses

Parentheses, also known as brackets, play an essential role in mathematical expressions. They indicate which operations should be performed first. In our exercise, the expression inside the parentheses is \((7-4)\). According to the BODMAS rule, you handle this part of the calculation first. It simplifies to 3, which then becomes part of the larger expression. Parentheses often serve to avoid ambiguity in calculations, guiding you step by step through the process. They act like a clue, showing you the priority of tasks in solving equations or expressions.

Exponents

Exponents are used to represent repeated multiplication of a number by itself. For instance, \(3^2\) means multiplying 3 by itself, resulting in 9. In our exercise, after solving the parentheses, the exponent is applied to the result. Following the BODMAS rule, exponents come after handling anything within parentheses. Recognizing and calculating exponents correctly is vital to maintaining the accuracy of your results, especially in more complex mathematical expressions where several operations occur.

Addition

Addition is one of the basic operations in mathematics and is quite straightforward. It involves finding the total or sum by combining numbers. In our example, addition is performed twice. First, you add the result of the squared calculation (9) to 3, then add this new result (12) to 15. According to the BODMAS rule, addition takes place after all operations inside parentheses and any exponents have been addressed. Ensuring you follow this order is crucial for obtaining the correct result efficiently.