The Expression $5(2+w)+6 W$ Is Simplified In Several Steps Below. For Each Step, Choose The Reason That Best Justifies It.$[ \begin{array}{|l|l|} \hline \text{Step} & \text{Reason} \ \hline 5(2+w)+6 W & \text{Given Expression}
Introduction
In mathematics, simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. The expression $5(2+w)+6 w$ is a simple example of an algebraic expression that can be simplified using various mathematical operations. In this article, we will break down the simplification process into several steps and analyze each step to understand the reasoning behind it.
Step 1: Distributive Property
The first step in simplifying the expression is to apply the distributive property, which states that for any real numbers a, b, and c, the following equation holds:
a(b + c) = ab + ac
Using this property, we can rewrite the expression as:
Reason: The distributive property is applied to expand the expression and make it easier to simplify.
Step 2: Combine Like Terms
The next step is to combine like terms, which involves adding or subtracting terms that have the same variable and exponent. In this case, we can combine the terms 5w and 6w:
Reason: Combining like terms helps to simplify the expression and make it easier to work with.
Step 3: Simplify the Expression
Now that we have combined like terms, we can simplify the expression further by evaluating the expression inside the parentheses:
Reason: Simplifying the expression inside the parentheses helps to reduce the complexity of the expression and make it easier to work with.
Step 4: Final Simplification
The final step is to simplify the expression by combining the constant term and the variable term:
Reason: The expression is already simplified, and no further simplification is possible.
Conclusion
In conclusion, the expression $5(2+w)+6 w$ can be simplified using the distributive property, combining like terms, and simplifying the expression. Each step in the simplification process is justified by the mathematical properties and rules that govern algebraic expressions.
Discussion
The simplification process of the expression $5(2+w)+6 w$ is a great example of how mathematical properties and rules can be applied to simplify complex expressions. By understanding and applying these properties and rules, we can simplify expressions and make them easier to work with.
Key Takeaways
- The distributive property can be used to expand expressions and make them easier to simplify.
- Combining like terms helps to simplify expressions and make them easier to work with.
- Simplifying expressions involves evaluating expressions inside parentheses and combining constant terms and variable terms.
Further Reading
For more information on algebraic expressions and simplification, please refer to the following resources:
References
Glossary
- Distributive Property: A mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.
- Like Terms: Terms that have the same variable and exponent.
- Simplifying Expressions: The process of reducing the complexity of an expression by applying mathematical properties and rules.
The Expression Simplification Process: A Q&A Article ===========================================================
Introduction
In our previous article, we explored the simplification process of the expression $5(2+w)+6 w$ using the distributive property, combining like terms, and simplifying the expression. In this article, we will answer some frequently asked questions related to the simplification process and provide additional insights into algebraic expressions.
Q&A
Q: What is the distributive property, and how is it used in simplifying expressions?
A: The distributive property is a mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac. It is used to expand expressions and make them easier to simplify. In the expression $5(2+w)+6 w$, the distributive property is used to expand the expression and make it easier to combine like terms.
Q: What are like terms, and how are they combined in simplifying expressions?
A: Like terms are terms that have the same variable and exponent. In the expression $5(2+w)+6 w$, the terms 5w and 6w are like terms because they both have the variable w and the exponent 1. Like terms are combined by adding or subtracting their coefficients.
Q: How do I know when to simplify an expression?
A: An expression should be simplified when it is in its simplest form, meaning that there are no like terms that can be combined. Simplifying an expression can make it easier to work with and can help to avoid errors.
Q: Can I simplify an expression by rearranging the terms?
A: No, an expression should not be simplified by rearranging the terms. Simplifying an expression involves applying mathematical properties and rules, such as the distributive property and combining like terms.
Q: What are some common mistakes to avoid when simplifying expressions?
A: Some common mistakes to avoid when simplifying expressions include:
- Not applying the distributive property when expanding expressions
- Not combining like terms when simplifying expressions
- Rearranging terms instead of applying mathematical properties and rules
- Not checking for errors when simplifying expressions
Q: How do I know if an expression is in its simplest form?
A: An expression is in its simplest form when there are no like terms that can be combined. To check if an expression is in its simplest form, look for terms that have the same variable and exponent and combine them.
Q: Can I use a calculator to simplify expressions?
A: Yes, a calculator can be used to simplify expressions. However, it is always a good idea to check the calculator's work by simplifying the expression manually.
Conclusion
In conclusion, simplifying expressions is an important skill in mathematics that can be used to solve equations and inequalities. By understanding the distributive property, combining like terms, and simplifying expressions, we can make expressions easier to work with and avoid errors.
Discussion
The simplification process of the expression $5(2+w)+6 w$ is a great example of how mathematical properties and rules can be applied to simplify complex expressions. By understanding and applying these properties and rules, we can simplify expressions and make them easier to work with.
Key Takeaways
- The distributive property can be used to expand expressions and make them easier to simplify.
- Combining like terms helps to simplify expressions and make them easier to work with.
- Simplifying expressions involves applying mathematical properties and rules, such as the distributive property and combining like terms.
- An expression should be simplified when it is in its simplest form, meaning that there are no like terms that can be combined.
Further Reading
For more information on algebraic expressions and simplification, please refer to the following resources:
References
Glossary
- Distributive Property: A mathematical property that states that for any real numbers a, b, and c, the following equation holds: a(b + c) = ab + ac.
- Like Terms: Terms that have the same variable and exponent.
- Simplifying Expressions: The process of reducing the complexity of an expression by applying mathematical properties and rules.