Simplify The Expression: $\[ 3p - (-5) + (2p) - 8 \\]

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Introduction

Simplifying algebraic expressions is a fundamental concept in mathematics, and it plays a crucial role in solving various mathematical problems. In this article, we will focus on simplifying the given expression: 3p - (-5) + (2p) - 8. We will use the rules of algebra to simplify the expression and provide a step-by-step solution.

Understanding the Expression

The given expression is 3p - (-5) + (2p) - 8. To simplify this expression, we need to understand the order of operations and the rules of algebra. The expression consists of four terms: 3p, -(-5), 2p, and -8.

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expressions inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate the Expressions Inside the Parentheses

The expression inside the parentheses is -(-5). To evaluate this expression, we need to follow the rule of algebra that states: -(-a) = a.

-(-5) = 5

Step 2: Rewrite the Expression

Now that we have evaluated the expression inside the parentheses, we can rewrite the expression as:

3p + 5 + (2p) - 8

Step 3: Combine Like Terms

The expression consists of two like terms: 3p and 2p. We can combine these terms by adding their coefficients.

3p + 2p = 5p

Step 4: Rewrite the Expression

Now that we have combined the like terms, we can rewrite the expression as:

5p + 5 - 8

Step 5: Combine the Constants

The expression consists of two constants: 5 and -8. We can combine these constants by adding them.

5 - 8 = -3

Step 6: Rewrite the Expression

Now that we have combined the constants, we can rewrite the expression as:

5p - 3

Conclusion

In this article, we simplified the given expression: 3p - (-5) + (2p) - 8. We followed the order of operations and used the rules of algebra to simplify the expression. The final simplified expression is 5p - 3.

Importance of Simplifying Algebraic Expressions

Simplifying algebraic expressions is an essential skill in mathematics. It helps us to:

  • Solve mathematical problems more efficiently
  • Understand the underlying structure of mathematical expressions
  • Identify patterns and relationships between variables
  • Make predictions and generalizations based on mathematical models

Tips for Simplifying Algebraic Expressions

Here are some tips for simplifying algebraic expressions:

  • Follow the order of operations (PEMDAS)
  • Use the rules of algebra to simplify expressions
  • Combine like terms
  • Simplify constants
  • Check your work for errors

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying algebraic expressions:

  • Failing to follow the order of operations (PEMDAS)
  • Not using the rules of algebra to simplify expressions
  • Not combining like terms
  • Not simplifying constants
  • Not checking your work for errors

Real-World Applications

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

  • Physics: Simplifying algebraic expressions is essential in physics, where mathematical models are used to describe the behavior of physical systems.
  • Engineering: Simplifying algebraic expressions is crucial in engineering, where mathematical models are used to design and optimize systems.
  • Economics: Simplifying algebraic expressions is important in economics, where mathematical models are used to analyze and predict economic behavior.

Conclusion

In conclusion, simplifying algebraic expressions is a fundamental concept in mathematics. It plays a crucial role in solving various mathematical problems and has many real-world applications. By following the order of operations and using the rules of algebra, we can simplify complex expressions and make predictions and generalizations based on mathematical models.

Introduction

In our previous article, we simplified the expression: 3p - (-5) + (2p) - 8. We followed the order of operations and used the rules of algebra to simplify the expression. In this article, we will answer some frequently asked questions (FAQs) related to simplifying algebraic expressions.

Q&A

Q1: What is the order of operations (PEMDAS)?

A1: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

  • Parentheses: Evaluate the expressions inside the parentheses.
  • Exponents: Evaluate any exponential expressions.
  • Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  • Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q2: What is the rule for simplifying expressions with negative coefficients?

A2: When we have an expression with a negative coefficient, we can simplify it by changing the sign of the coefficient. For example, -(-5) = 5.

Q3: How do we combine like terms?

A3: To combine like terms, we add or subtract the coefficients of the terms. For example, 3p + 2p = 5p.

Q4: What is the difference between a constant and a variable?

A4: A constant is a value that does not change, such as 5 or -8. A variable is a value that can change, such as p or x.

Q5: How do we simplify expressions with fractions?

A5: To simplify expressions with fractions, we can multiply both the numerator and the denominator by the same value to eliminate the fraction. For example, (3/4) + (2/4) = (5/4).

Q6: What is the importance of simplifying algebraic expressions?

A6: Simplifying algebraic expressions is essential in mathematics because it helps us to:

  • Solve mathematical problems more efficiently
  • Understand the underlying structure of mathematical expressions
  • Identify patterns and relationships between variables
  • Make predictions and generalizations based on mathematical models

Q7: How do we check our work for errors?

A7: To check our work for errors, we can:

  • Use a calculator to evaluate the expression
  • Plug in values for the variables to see if the expression holds true
  • Simplify the expression step by step to ensure that we have not made any mistakes

Q8: What are some common mistakes to avoid when simplifying algebraic expressions?

A8: Some common mistakes to avoid when simplifying algebraic expressions include:

  • Failing to follow the order of operations (PEMDAS)
  • Not using the rules of algebra to simplify expressions
  • Not combining like terms
  • Not simplifying constants
  • Not checking your work for errors

Conclusion

In conclusion, simplifying algebraic expressions is a fundamental concept in mathematics. By following the order of operations and using the rules of algebra, we can simplify complex expressions and make predictions and generalizations based on mathematical models. We hope that this Q&A article has helped to clarify any questions you may have had about simplifying algebraic expressions.

Additional Resources

If you are looking for additional resources to help you with simplifying algebraic expressions, here are some suggestions:

  • Khan Academy: Algebra
  • Mathway: Algebra Calculator
  • Wolfram Alpha: Algebra Solver

Final Thoughts

Simplifying algebraic expressions is an essential skill in mathematics. By practicing and mastering this skill, you will be able to solve mathematical problems more efficiently and make predictions and generalizations based on mathematical models. Remember to always follow the order of operations and use the rules of algebra to simplify expressions.