Can You Help With This Answer 4 + (5² - 2³) =

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Introduction

In mathematics, algebraic expressions are a fundamental concept that helps us solve various problems. These expressions involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. In this article, we will focus on solving a specific algebraic expression: 4 + (5² - 2³). We will break down the solution step by step, using the order of operations (PEMDAS) to ensure accuracy.

Understanding the Order of Operations

Before we dive into the solution, it's essential to understand the order of operations, also known as PEMDAS. This acronym stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next (e.g., 2³).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Breaking Down the Expression

Now that we understand the order of operations, let's break down the given expression: 4 + (5² - 2³).

Step 1: Evaluate the Exponents

The expression contains two exponential terms: 5² and 2³. We will evaluate these terms first.

  • 5² = 5 × 5 = 25
  • 2³ = 2 × 2 × 2 = 8

Step 2: Evaluate the Expression Inside the Parentheses

Now that we have evaluated the exponents, we can rewrite the expression as 4 + (25 - 8).

Step 3: Perform the Subtraction

Next, we will perform the subtraction operation inside the parentheses.

  • 25 - 8 = 17

Step 4: Add 4 to the Result

Finally, we will add 4 to the result of the expression inside the parentheses.

  • 4 + 17 = 21

Conclusion

In this article, we solved the algebraic expression 4 + (5² - 2³) using the order of operations (PEMDAS). We broke down the solution into four steps, evaluating the exponents, the expression inside the parentheses, the subtraction operation, and finally, the addition operation. By following the order of operations, we arrived at the final answer: 21.

Real-World Applications

Algebraic expressions like the one we solved in this article have numerous real-world applications. For example, in finance, algebraic expressions are used to calculate interest rates, investment returns, and other financial metrics. In science, algebraic expressions are used to model complex systems, such as population growth, chemical reactions, and electrical circuits.

Tips and Tricks

When solving algebraic expressions, it's essential to follow the order of operations (PEMDAS) to ensure accuracy. Here are some additional tips and tricks to help you solve algebraic expressions like a pro:

  • Use parentheses: Parentheses help to clarify the order of operations and prevent errors.
  • Evaluate exponents first: Exponents are evaluated before any multiplication or division operations.
  • Perform multiplication and division from left to right: When there are multiple multiplication or division operations, perform them from left to right.
  • Add and subtract from left to right: Finally, perform any addition or subtraction operations from left to right.

Common Mistakes to Avoid

When solving algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations: Failing to follow the order of operations (PEMDAS) can lead to incorrect answers.
  • Not evaluating exponents first: Failing to evaluate exponents first can lead to incorrect answers.
  • Not performing multiplication and division from left to right: Failing to perform multiplication and division operations from left to right can lead to incorrect answers.
  • Not adding and subtracting from left to right: Failing to perform addition and subtraction operations from left to right can lead to incorrect answers.

Conclusion

In conclusion, solving algebraic expressions like 4 + (5² - 2³) requires a clear understanding of the order of operations (PEMDAS). By following the order of operations and breaking down the solution into manageable steps, we can arrive at the correct answer. Remember to use parentheses, evaluate exponents first, perform multiplication and division from left to right, and add and subtract from left to right to ensure accuracy.