Simplify This Expression: $4p + 9 + (-7p) + 2$A. $3p + 7$ B. $-3p + 11$ C. $3p + 11$ D. $11p + 11$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression, $4p + 9 + (-7p) + 2$, and explore the different methods and techniques involved.

Understanding the Expression

The given expression is $4p + 9 + (-7p) + 2$. To simplify this expression, we need to combine like terms, which are terms that have the same variable raised to the same power. In this case, the like terms are $4p$ and $-7p$, which are both terms with the variable $p$.

Combining Like Terms

To combine like terms, we need to add or subtract the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficient of $4p$ is 4, and the coefficient of $-7p$ is -7.

4p + (-7p) = (4 - 7)p
= -3p

Now that we have combined the like terms, the expression becomes $-3p + 9 + 2$.

Simplifying the Expression

To simplify the expression further, we need to combine the constant terms, which are the terms that do not have a variable. In this case, the constant terms are 9 and 2.

9 + 2 = 11

Now that we have combined the constant terms, the expression becomes $-3p + 11$.

Conclusion

In conclusion, the simplified expression is $-3p + 11$. This is the final answer to the problem.

Answer Key

The correct answer is B. $-3p + 11$.

Tips and Tricks

• When combining like terms, make sure to add or subtract the coefficients of the terms.
• When simplifying an expression, make sure to combine the constant terms.
• Use the distributive property to simplify expressions with multiple terms.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

• Science and Engineering: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.
• Computer Science: Algebraic expressions are used to write algorithms and solve problems in computer science.

Common Mistakes

• Not combining like terms: Failing to combine like terms can lead to incorrect answers.
• Not simplifying the expression: Failing to simplify the expression can lead to incorrect answers.
• Using the wrong method: Using the wrong method to simplify an expression can lead to incorrect answers.

Conclusion

Introduction

In our previous article, we explored the concept of simplifying algebraic expressions and provided a step-by-step guide on how to simplify the expression $4p + 9 + (-7p) + 2$. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable raised to the same power. Unlike terms are terms that have different variables or variables raised to different powers.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable.

Q: What is the distributive property?

A: The distributive property is a rule that allows you to multiply a single term by multiple terms. It is represented by the equation: a(b + c) = ab + ac.

Q: How do I simplify an expression with multiple terms?

A: To simplify an expression with multiple terms, you need to combine like terms and use the distributive property to simplify the expression.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an expression. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first and then simplify the expression.

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

A: A coefficient is a number that is multiplied by a variable. A constant is a number that is not multiplied by a variable.

Q: How do I simplify an expression with variables and constants?

A: To simplify an expression with variables and constants, you need to combine like terms and use the distributive property to simplify the expression.

Q: What is the final answer to the expression $4p + 9 + (-7p) + 2$?

A: The final answer to the expression $4p + 9 + (-7p) + 2$ is $-3p + 11$.

Tips and Tricks

• Always combine like terms first.
• Use the distributive property to simplify expressions with multiple terms.
• Evaluate expressions inside parentheses first.
• Use the order of operations to simplify expressions.

Common Mistakes

• Not combining like terms.
• Not using the distributive property to simplify expressions with multiple terms.
• Not evaluating expressions inside parentheses first.
• Not using the order of operations to simplify expressions.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for students and professionals alike. By following the steps outlined in this article and using the tips and tricks provided, you can simplify expressions and solve problems with confidence. Remember to combine like terms, use the distributive property, and evaluate expressions inside parentheses first. With practice and patience, you can become proficient in simplifying algebraic expressions and tackle complex problems with ease.