Determine If Dwayne's Work Is Correct In Evaluating The Expression:$\[ \begin{array}{l} 3+5 \cdot\left[4^2-(5-2)^2\right] \\ = 3+5 \cdot\left[4^2-3^2\right] \\ = 3+5 \cdot[16-9] \\ = \text{Step 1} \\ = 3+5 \cdot 7 \\ = \text{Step 2} \\ =

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Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them correctly is crucial for solving mathematical problems. In this article, we will determine if Dwayne's work is correct in evaluating the expression: 3+5⋅[42−(5−2)2]3+5 \cdot\left[4^2-(5-2)^2\right]. We will break down the expression step by step and provide a detailed explanation of each step.

Step 1: Evaluate the Exponents

The first step in evaluating the expression is to calculate the exponents. In this case, we have two exponents: 424^2 and (5−2)2(5-2)^2. To evaluate these exponents, we need to follow the order of operations (PEMDAS):

  • Evaluate the expressions inside the parentheses: (5−2)2=32(5-2)^2 = 3^2
  • Calculate the exponent: 42=164^2 = 16 and 32=93^2 = 9
# Step 1: Evaluate the Exponents
## 4^2 = 16
## (5-2)^2 = 3^2 = 9

Step 2: Subtract the Exponents

Now that we have evaluated the exponents, we can subtract them:

16−9=716 - 9 = 7

# Step 2: Subtract the Exponents
## 16 - 9 = 7

Step 3: Multiply 5 by the Result

Next, we need to multiply 5 by the result of the subtraction:

5⋅7=355 \cdot 7 = 35

# Step 3: Multiply 5 by the Result
## 5 \cdot 7 = 35

Step 4: Add 3 to the Result

Finally, we need to add 3 to the result of the multiplication:

3+35=383 + 35 = 38

# Step 4: Add 3 to the Result
## 3 + 35 = 38

Conclusion

In conclusion, Dwayne's work is correct in evaluating the expression: 3+5⋅[42−(5−2)2]3+5 \cdot\left[4^2-(5-2)^2\right]. The correct evaluation of the expression is:

3+5⋅[42−(5−2)2]=3+5⋅7=383+5 \cdot\left[4^2-(5-2)^2\right] = 3+5 \cdot 7 = 38

Discussion

The expression 3+5⋅[42−(5−2)2]3+5 \cdot\left[4^2-(5-2)^2\right] is a classic example of an algebraic expression that requires careful evaluation. The order of operations (PEMDAS) is crucial in evaluating this expression, and following the correct order of operations ensures that the expression is evaluated correctly.

Common Mistakes

When evaluating algebraic expressions, it is easy to make mistakes. Some common mistakes include:

  • Not following the order of operations (PEMDAS)
  • Not evaluating exponents correctly
  • Not subtracting or adding correctly

To avoid these mistakes, it is essential to follow the order of operations (PEMDAS) and to evaluate exponents and expressions correctly.

Tips and Tricks

Here are some tips and tricks for evaluating algebraic expressions:

  • Always follow the order of operations (PEMDAS)
  • Evaluate exponents and expressions correctly
  • Use parentheses to group expressions and avoid confusion
  • Check your work carefully to avoid mistakes

By following these tips and tricks, you can evaluate algebraic expressions correctly and avoid common mistakes.

Conclusion

Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them correctly is crucial for solving mathematical problems. In this article, we will provide a Q&A guide to help you evaluate algebraic expressions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

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

Q: How do I evaluate exponents?

A: To evaluate exponents, you need to follow the order of operations (PEMDAS). For example, to evaluate the expression 2^3, you would:

  • Raise 2 to the power of 3 (2^3 = 8)
  • Evaluate any expressions inside parentheses
  • Evaluate any multiplication and division operations
  • Finally, evaluate any addition and subtraction operations

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

For example:

  • 2 × 3 = 6 (multiplication)
  • 6 ÷ 2 = 3 (division)

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations (PEMDAS). For example, to evaluate the expression 2 × 3 + 4, you would:

  • Multiply 2 and 3 (2 × 3 = 6)
  • Add 4 to the result (6 + 4 = 10)

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different rules. Addition involves adding two or more numbers together, while subtraction involves subtracting one number from another.

For example:

  • 2 + 3 = 5 (addition)
  • 5 - 2 = 3 (subtraction)

Q: How do I evaluate expressions with parentheses?

A: To evaluate expressions with parentheses, you need to follow the order of operations (PEMDAS). For example, to evaluate the expression (2 + 3) × 4, you would:

  • Evaluate the expression inside the parentheses (2 + 3 = 5)
  • Multiply 5 by 4 (5 × 4 = 20)

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change.

For example:

  • x is a variable (its value can change)
  • 5 is a constant (its value does not change)

Q: How do I evaluate expressions with variables?

A: To evaluate expressions with variables, you need to follow the order of operations (PEMDAS). For example, to evaluate the expression 2x + 3, you would:

  • Multiply 2 by the value of x (2x)
  • Add 3 to the result (2x + 3)

Conclusion

In conclusion, evaluating algebraic expressions is a crucial skill in mathematics. By following the order of operations (PEMDAS) and understanding the rules of multiplication, division, addition, and subtraction, you can evaluate algebraic expressions correctly. Remember to always follow the order of operations (PEMDAS), evaluate exponents and expressions correctly, and check your work carefully to avoid mistakes.

Common Mistakes

When evaluating algebraic expressions, it is easy to make mistakes. Some common mistakes include:

  • Not following the order of operations (PEMDAS)
  • Not evaluating exponents correctly
  • Not subtracting or adding correctly
  • Not using parentheses correctly

To avoid these mistakes, it is essential to follow the order of operations (PEMDAS) and to evaluate exponents and expressions correctly.

Tips and Tricks

Here are some tips and tricks for evaluating algebraic expressions:

  • Always follow the order of operations (PEMDAS)
  • Evaluate exponents and expressions correctly
  • Use parentheses to group expressions and avoid confusion
  • Check your work carefully to avoid mistakes
  • Practice, practice, practice!

By following these tips and tricks, you can evaluate algebraic expressions correctly and avoid common mistakes.