Simplify The Expression.${ 5k - (2k - 4) }$

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 the expression 5k - (2k - 4) using basic algebraic rules and techniques. By the end of this guide, you will be able to simplify complex expressions with ease.

Understanding the Expression

The given expression is 5k - (2k - 4). To simplify this expression, we need to understand the order of operations (PEMDAS) and the properties of algebraic expressions. The expression consists of two terms: 5k and (2k - 4). The subtraction of (2k - 4) from 5k is the main operation we need to focus on.

Distributive Property

To simplify the expression, we will use the distributive property, which states that for any real numbers a, b, and c, a(b - c) = ab - ac. In this case, we can rewrite the expression as 5k - 2k + 4.

Applying the Distributive Property

Now, let's apply the distributive property to the expression 5k - (2k - 4). We can rewrite it as:

5k - 2k + 4

Combining Like Terms

The next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: 5k and -2k. We can combine these terms by adding their coefficients.

Simplifying the Expression

Now, let's simplify the expression by combining like terms:

5k - 2k + 4

Combine like terms:

3k + 4

Final Answer

The simplified expression is 3k + 4.

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By understanding the order of operations and applying basic algebraic rules and techniques, we can simplify complex expressions with ease. In this article, we focused on simplifying the expression 5k - (2k - 4) using the distributive property and combining like terms. By following these steps, you can simplify any algebraic expression with confidence.

Frequently Asked Questions

• What is the distributive property? The distributive property is a basic algebraic rule that states that for any real numbers a, b, and c, a(b - c) = ab - ac.
• How do I simplify an algebraic expression? To simplify an algebraic expression, you need to apply the order of operations (PEMDAS) and use basic algebraic rules and techniques such as the distributive property and combining like terms.
• What are like terms? Like terms are terms that have the same variable raised to the same power.

Additional Resources

• Algebraic expressions: A comprehensive guide to algebraic expressions, including definitions, examples, and practice problems.
• Distributive property: A detailed explanation of the distributive property, including examples and practice problems.
• Combining like terms: A step-by-step guide to combining like terms, including examples and practice problems.

Final Thoughts

Simplifying algebraic expressions is an essential skill for students and professionals alike. By understanding the order of operations and applying basic algebraic rules and techniques, we can simplify complex expressions with ease. In this article, we focused on simplifying the expression 5k - (2k - 4) using the distributive property and combining like terms. By following these steps, you can simplify any algebraic expression with confidence.

Introduction

Simplifying algebraic expressions is a crucial skill for students and professionals alike. In our previous article, we provided a step-by-step guide to simplifying the expression 5k - (2k - 4) using the distributive property and combining like terms. However, we understand that you may still have questions about algebraic expression simplification. In this article, we will address some of the most frequently asked questions about simplifying algebraic expressions.

Q&A

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

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It is essential to follow the order of operations to simplify algebraic expressions correctly.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to apply the order of operations (PEMDAS) and use basic algebraic rules and techniques such as the distributive property and combining like terms. Start by evaluating any expressions inside parentheses, then evaluate any exponents, and finally perform any multiplication and division operations from left to right. Finally, perform any addition and subtraction operations from left to right.

Q: What is the distributive property?

A: The distributive property is a basic algebraic rule that states that for any real numbers a, b, and c, a(b - c) = ab - ac. It allows us to distribute a single term across the terms inside the parentheses.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable raised to the same power. Then, add or subtract the coefficients of these terms to simplify the expression.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 4x are like terms because they both have the variable x raised to the power of 1.

Q: Can I simplify an algebraic expression by rearranging the terms?

A: No, you cannot simplify an algebraic expression by rearranging the terms. Simplifying an algebraic expression involves applying the order of operations (PEMDAS) and using basic algebraic rules and techniques such as the distributive property and combining like terms.

Q: How do I know when an algebraic expression is simplified?

A: An algebraic expression is simplified when it cannot be simplified further using the order of operations (PEMDAS) and basic algebraic rules and techniques. In other words, if you have applied all the necessary rules and techniques and the expression still cannot be simplified, then it is simplified.

Q: Can I use a calculator to simplify an algebraic expression?

A: Yes, you can use a calculator to simplify an algebraic expression. However, it is essential to understand the underlying algebraic rules and techniques to ensure that you are using the calculator correctly.

Conclusion

Simplifying algebraic expressions is a crucial skill for students and professionals alike. By understanding the order of operations (PEMDAS) and applying basic algebraic rules and techniques such as the distributive property and combining like terms, you can simplify complex expressions with ease. In this article, we addressed some of the most frequently asked questions about simplifying algebraic expressions. We hope that this article has provided you with a better understanding of algebraic expression simplification.

Additional Resources

• Algebraic expressions: A comprehensive guide to algebraic expressions, including definitions, examples, and practice problems.
• Distributive property: A detailed explanation of the distributive property, including examples and practice problems.
• Combining like terms: A step-by-step guide to combining like terms, including examples and practice problems.
• Order of operations (PEMDAS): A detailed explanation of the order of operations, including examples and practice problems.

Final Thoughts

Simplifying algebraic expressions is an essential skill for students and professionals alike. By understanding the order of operations (PEMDAS) and applying basic algebraic rules and techniques such as the distributive property and combining like terms, you can simplify complex expressions with ease. We hope that this article has provided you with a better understanding of algebraic expression simplification.