Select The Correct Answer.Simplify: 3 ⋅ 3 2 + 8 ÷ 2 − ( 4 + 3 3 \cdot 3^2 + 8 \div 2 - (4 + 3 3 ⋅ 3 2 + 8 ÷ 2 − ( 4 + 3 ]A. 24 B. 30 C. 32 D. 23

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students to master. In this article, we will guide you through the process of simplifying a given algebraic expression, step by step. We will use the expression $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$ as an example.

Understanding the Order of Operations

Before we start simplifying the expression, it's essential to understand the order of operations. The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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.

Simplifying the Expression

Now that we have a good understanding of the order of operations, let's simplify the expression $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$.

Step 1: Evaluate Expressions Inside Parentheses

The first step is to evaluate the expression inside the parentheses: $(4 + 3)$. This is a simple addition problem, and the result is $7$.

# Evaluate expression inside parentheses
parentheses = 4 + 3
print(parentheses)  # Output: 7

Step 2: Evaluate Exponential Expressions

The next step is to evaluate any exponential expressions. In this case, we have $3^2$, which is equal to $9$.

# Evaluate exponential expression
exponent = 3 ** 2
print(exponent)  # Output: 9

Step 3: Multiply and Divide

Now that we have evaluated the expressions inside the parentheses and the exponential expression, we can multiply and divide. We have $3 \cdot 9$ and $8 \div 2$. The result of the multiplication is $27$, and the result of the division is $4$.

# Multiply and divide
multiply = 3 * 9
divide = 8 / 2
print(multiply)  # Output: 27
print(divide)  # Output: 4

Step 4: Add and Subtract

Finally, we can add and subtract. We have $27 + 4 - 7$. The result of the addition is $31$, and the result of the subtraction is $24$.

# Add and subtract
add = 27 + 4
subtract = add - 7
print(subtract)  # Output: 24

Conclusion

In this article, we have simplified the algebraic expression $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$ step by step. We have followed the order of operations, evaluated expressions inside parentheses, exponential expressions, multiplied and divided, and finally added and subtracted. The final result is $24$.

Answer

The correct answer is A. 24.

Discussion

This problem is a great example of how to simplify algebraic expressions using the order of operations. It's essential to follow the order of operations to ensure that we get the correct result. If you have any questions or need further clarification, please don't hesitate to ask.

Additional Resources

If you want to learn more about algebraic expressions and the order of operations, here are some additional resources:

• Khan Academy: Algebraic Expressions
• Mathway: Algebraic Expressions
• Wolfram Alpha: Algebraic Expressions

Final Thoughts

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Introduction

In our previous article, we simplified the algebraic expression $3 \cdot 3^2 + 8 \div 2 - (4 + 3)$ step by step. We followed the order of operations, evaluated expressions inside parentheses, exponential expressions, multiplied and divided, and finally added and subtracted. In this article, we will answer some frequently asked questions about simplifying algebraic expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is as follows:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
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.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that we get the correct result. If we don't follow the order of operations, we may get a different result, which can lead to errors in our calculations.

Q: How do I evaluate expressions inside parentheses?

A: To evaluate expressions inside parentheses, we need to follow the order of operations. We need to evaluate any exponential expressions, multiplication and division operations, and finally addition and subtraction operations.

Q: What is an exponential expression?

A: An exponential expression is an expression that involves raising a number to a power. For example, $3^2$ is an exponential expression.

Q: How do I evaluate exponential expressions?

A: To evaluate exponential expressions, we need to raise the base number to the power indicated. For example, $3^2$ is equal to $9$.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they are performed in different ways. Multiplication involves adding a number a certain number of times, while division involves finding the quotient of two numbers.

Q: How do I evaluate multiplication and division operations?

A: To evaluate multiplication and division operations, we need to follow the order of operations. We need to evaluate any exponential expressions, and then perform the multiplication and division operations from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they are performed in different ways. Addition involves finding the sum of two or more numbers, while subtraction involves finding the difference between two numbers.

Q: How do I evaluate addition and subtraction operations?

A: To evaluate addition and subtraction operations, we need to follow the order of operations. We need to evaluate any exponential expressions, multiplication and division operations, and then perform the addition and subtraction operations from left to right.

Q: What if I have multiple operations in an expression?

A: If you have multiple operations in an expression, you need to follow the order of operations. You need to evaluate any exponential expressions, multiplication and division operations, and then perform the addition and subtraction operations from left to right.

Conclusion

In this article, we have answered some frequently asked questions about simplifying algebraic expressions. We have covered the order of operations, evaluating expressions inside parentheses, exponential expressions, multiplication and division operations, addition and subtraction operations, and multiple operations in an expression. We hope this article has been helpful in answering your questions about simplifying algebraic expressions.

Additional Resources

If you want to learn more about algebraic expressions and the order of operations, here are some additional resources:

• Khan Academy: Algebraic Expressions
• Mathway: Algebraic Expressions
• Wolfram Alpha: Algebraic Expressions

Final Thoughts

Simplifying algebraic expressions is an essential skill for students to master. By following the order of operations and evaluating expressions step by step, we can ensure that we get the correct result. We hope this article has been helpful in answering your questions about simplifying algebraic expressions. If you have any further questions or need further clarification, please don't hesitate to ask.