Completely Simplify The Expression: 14 Z − 13 + 11 Z − 2 14z - 13 + 11z - 2 14 Z − 13 + 11 Z − 2 Answer: □ \square □

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Understanding the Basics of Algebraic Expressions

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 given expression: 14z−13+11z−214z - 13 + 11z - 2. By the end of this article, you will have a clear understanding of how to simplify algebraic expressions and be able to apply this knowledge to various mathematical problems.

What are Algebraic Expressions?

An algebraic expression is a combination of variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using mathematical symbols. Algebraic expressions can be simple or complex, and they can be used to solve equations, inequalities, and other mathematical problems.

The Importance of Simplifying Algebraic Expressions

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

  • Reduce complexity: Simplifying expressions makes them easier to understand and work with.
  • Identify patterns: By simplifying expressions, you can identify patterns and relationships between variables.
  • Solve equations: Simplifying expressions is a crucial step in solving equations and inequalities.
  • Make calculations easier: Simplified expressions make calculations easier and faster.

Step-by-Step Guide to Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms, removing parentheses, and applying mathematical operations. Here's a step-by-step guide to simplifying the given expression:

Step 1: Combine Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, the like terms are 14z14z and 11z11z. To combine like terms, we add or subtract their coefficients.

# Define the variables
z = 'z'
expression = '14z - 13 + 11z - 2'

simplified_expression = '25z - 15'

Step 2: Remove Parentheses

Parentheses are used to group terms or expressions. In the given expression, there are no parentheses to remove.

Step 3: Apply Mathematical Operations

In the given expression, there are no mathematical operations to apply.

Simplifying the Expression: 14z−13+11z−214z - 13 + 11z - 2

Now that we have combined like terms, removed parentheses, and applied mathematical operations, we can simplify the expression.

# Simplify the expression
simplified_expression = '25z - 15'

Conclusion

Simplifying algebraic expressions is a crucial skill in mathematics. By combining like terms, removing parentheses, and applying mathematical operations, we can simplify expressions and make calculations easier. In this article, we simplified the expression 14z−13+11z−214z - 13 + 11z - 2 and arrived at the simplified expression 25z−1525z - 15. We hope this article has provided you with a clear understanding of how to simplify algebraic expressions and has helped you to develop your mathematical skills.

Frequently Asked Questions

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients.

Q: Why is simplifying algebraic expressions important?

A: Simplifying algebraic expressions is important because it helps to reduce complexity, identify patterns, solve equations, and make calculations easier.

Q: How do I remove parentheses?

A: To remove parentheses, you simply remove the parentheses and perform the operations inside.

Q: How do I apply mathematical operations?

A: To apply mathematical operations, you perform the operations indicated in the expression, such as addition, subtraction, multiplication, and division.

Glossary of Terms

  • Algebraic expression: A combination of variables, constants, and mathematical operations.
  • Like terms: Terms that have the same variable raised to the same power.
  • Coefficient: A number that is multiplied by a variable.
  • Parentheses: Symbols used to group terms or expressions.
  • Mathematical operation: An operation that is performed on variables or constants, such as addition, subtraction, multiplication, and division.

References

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Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, in the expression 2x+3x2x + 3x, the terms 2x2x and 3x3x are like terms because they both have the variable xx raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. For example, in the expression 2x+3x2x + 3x, you can combine the like terms by adding their coefficients: 2x+3x=5x2x + 3x = 5x.

Q: Why is simplifying algebraic expressions important?

A: Simplifying algebraic expressions is important because it helps to reduce complexity, identify patterns, solve equations, and make calculations easier. By simplifying expressions, you can make it easier to work with them and understand their relationships.

Q: How do I remove parentheses?

A: To remove parentheses, you simply remove the parentheses and perform the operations inside. For example, in the expression (2x+3x)(2x + 3x), you can remove the parentheses by adding the terms inside: 2x+3x=5x2x + 3x = 5x.

Q: How do I apply mathematical operations?

A: To apply mathematical operations, you perform the operations indicated in the expression, such as addition, subtraction, multiplication, and division. For example, in the expression 2x+3x2x + 3x, you can apply the addition operation by adding the terms: 2x+3x=5x2x + 3x = 5x.

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 working with expressions that contain multiple operations. The order of operations is:

  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: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, you can follow these steps:

  1. Combine like terms: Combine any like terms in the expression.
  2. Simplify the fraction: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
  3. Remove any common factors: Remove any common factors between the numerator and denominator.

Q: How do I simplify expressions with decimals?

A: To simplify expressions with decimals, you can follow these steps:

  1. Combine like terms: Combine any like terms in the expression.
  2. Round the decimals: Round the decimals to the desired number of decimal places.
  3. Remove any common factors: Remove any common factors between the numerator and denominator.

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

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

  • Not combining like terms: Failing to combine like terms can lead to incorrect simplifications.
  • Not removing parentheses: Failing to remove parentheses can lead to incorrect simplifications.
  • Not applying mathematical operations correctly: Failing to apply mathematical operations correctly can lead to incorrect simplifications.
  • Not checking for common factors: Failing to check for common factors can lead to incorrect simplifications.

Q: How can I practice simplifying algebraic expressions?

A: You can practice simplifying algebraic expressions by:

  • Working through examples: Work through examples of simplifying algebraic expressions to practice your skills.
  • Using online resources: Use online resources, such as math websites and apps, to practice simplifying algebraic expressions.
  • Taking practice tests: Take practice tests to assess your skills and identify areas for improvement.
  • Seeking help: Seek help from a teacher, tutor, or classmate if you are struggling with simplifying algebraic expressions.

Q: What are some real-world applications of simplifying algebraic expressions?

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

  • Science and engineering: Simplifying algebraic expressions is used in science and engineering to model and analyze complex systems.
  • Finance: Simplifying algebraic expressions is used in finance to calculate interest rates and investment returns.
  • Computer science: Simplifying algebraic expressions is used in computer science to optimize algorithms and data structures.
  • Data analysis: Simplifying algebraic expressions is used in data analysis to identify patterns and trends in data.

Q: How can I use simplifying algebraic expressions in my daily life?

A: You can use simplifying algebraic expressions in your daily life by:

  • Using algebraic expressions to model real-world problems: Use algebraic expressions to model real-world problems, such as calculating the cost of a product or the time it takes to complete a task.
  • Simplifying complex expressions: Simplify complex expressions to make them easier to understand and work with.
  • Identifying patterns and relationships: Use simplifying algebraic expressions to identify patterns and relationships between variables.
  • Making calculations easier: Use simplifying algebraic expressions to make calculations easier and faster.