Add The Expressions: ( − 8 P + 7 ) + ( P − 8 (-8p + 7) + (p - 8 ( − 8 P + 7 ) + ( P − 8 ]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is a crucial skill to master. In this article, we will focus on simplifying the expression $(-8p + 7) + (p - 8)$. We will break down the steps involved in simplifying this expression and provide a clear understanding of the process.

Understanding the Expression

The given expression is $(-8p + 7) + (p - 8)$. This expression consists of two terms, each containing a variable $p$ and a constant. To simplify this expression, we need to combine like terms, which means combining the terms that have the same variable.

Step 1: Distribute the Negative Sign

The first step in simplifying the expression is to distribute the negative sign to the terms inside the second set of parentheses. This will change the sign of each term inside the parentheses.

(-8p + 7) + (-p + 8)

Step 2: Combine Like Terms

Now that we have distributed the negative sign, we can combine like terms. The like terms in this expression are the terms that have the same variable, which is $p$. We can combine the terms with the variable $p$ by adding or subtracting their coefficients.

(-8p - p) + (7 + 8)

Step 3: Simplify the Expression

Now that we have combined like terms, we can simplify the expression by evaluating the terms. The expression can be simplified as follows:

-9p + 15

Conclusion

Simplifying algebraic expressions is an essential skill in mathematics. By following the steps outlined in this article, we can simplify the expression $(-8p + 7) + (p - 8)$. The simplified expression is $-9p + 15$. This expression can be used in a variety of mathematical applications, such as solving equations and graphing functions.

Tips and Tricks

• When simplifying algebraic expressions, it is essential to combine like terms.
• Distributing the negative sign to the terms inside the parentheses can help simplify the expression.
• Evaluating the terms after combining like terms can help simplify the expression further.

Real-World Applications

Simplifying algebraic expressions has numerous real-world applications. Some examples include:

• Physics: Simplifying algebraic expressions is essential in physics, where equations are used to describe the motion of objects.
• Engineering: Simplifying algebraic expressions is crucial in engineering, where equations are used to design and optimize systems.
• Computer Science: Simplifying algebraic expressions is essential in computer science, where equations are used to model and analyze complex systems.

Common Mistakes

• Not distributing the negative sign: Failing to distribute the negative sign to the terms inside the parentheses can lead to incorrect simplification of the expression.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplification of the expression.
• Not evaluating the terms: Failing to evaluate the terms after combining like terms can lead to incorrect simplification of the expression.

Conclusion

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics. In our previous article, we provided a step-by-step guide on how to simplify the expression $(-8p + 7) + (p - 8)$. In this article, we will provide a Q&A guide to help you understand the concept of simplifying algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. Algebraic expressions are used to represent relationships between variables and constants.

Q: What is the purpose of simplifying algebraic expressions?

A: The purpose of simplifying algebraic expressions is to make them easier to work with. Simplifying algebraic expressions can help you:

• Solve equations and inequalities
• Graph functions
• Analyze and model real-world problems

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Distribute the negative sign to the terms inside the parentheses.
2. Combine like terms.
3. Evaluate the terms after combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ and the same exponent.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, $2x + 5x = (2 + 5)x = 7x$.

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

A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I evaluate the terms after combining like terms?

A: To evaluate the terms after combining like terms, simply add or subtract the coefficients of the like terms. For example, $2x + 5x = 7x$.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

• Not distributing the negative sign to the terms inside the parentheses.
• Not combining like terms.
• Not evaluating the terms after combining like terms.

Q: How do I apply simplifying algebraic expressions in real-world problems?

A: Simplifying algebraic expressions is essential in many real-world applications, including:

• Physics: Simplifying algebraic expressions is used to describe the motion of objects.
• Engineering: Simplifying algebraic expressions is used to design and optimize systems.
• Computer Science: Simplifying algebraic expressions is used to model and analyze complex systems.

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics. By following the steps outlined in this article, you can simplify algebraic expressions and apply them to real-world problems. Remember to avoid common mistakes and practice simplifying algebraic expressions to become proficient in this skill.

Tips and Tricks

• Practice simplifying algebraic expressions regularly to become proficient in this skill.
• Use online resources and tools to help you simplify algebraic expressions.
• Apply simplifying algebraic expressions to real-world problems to see the practical applications of this skill.

Real-World Applications

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

• Physics: Simplifying algebraic expressions is used to describe the motion of objects.
• Engineering: Simplifying algebraic expressions is used to design and optimize systems.
• Computer Science: Simplifying algebraic expressions is used to model and analyze complex systems.

Common Mistakes

• Not distributing the negative sign: Failing to distribute the negative sign to the terms inside the parentheses can lead to incorrect simplification of the expression.
• Not combining like terms: Failing to combine like terms can lead to incorrect simplification of the expression.
• Not evaluating the terms: Failing to evaluate the terms after combining like terms can lead to incorrect simplification of the expression.