Simplify The Following Expression By Combining Like Terms:${ 2m^2 - M + 4m^2 + 8m } E N T E R T H E N U M B E R S T H A T B E L O N G I N T H E B O X E S : Enter The Numbers That Belong In The Boxes: E N T Er T H E N U Mb Ers T Ha T B E L O N G In T H E B O X Es : { [\ ?\ ]m^2 + [\ \square\ ]m \}
Introduction
Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill to master. In this article, we will focus on simplifying a given expression by combining like terms. We will break down the process into manageable steps and provide a clear explanation of each step.
Understanding Like Terms
Like terms are algebraic expressions that have the same variable raised to the same power. In other words, they are terms that have the same base and exponent. For example, 2m^2 and 4m^2 are like terms because they both have the variable m raised to the power of 2.
The Given Expression
The given expression is:
2m^2 - m + 4m^2 + 8m
Our goal is to simplify this expression by combining like terms.
Step 1: Identify Like Terms
The first step is to identify the like terms in the given expression. We can see that there are two terms with the variable m raised to the power of 2: 2m^2 and 4m^2. These two terms are like terms because they have the same base and exponent.
Step 2: Combine Like Terms
Now that we have identified the like terms, we can combine them by adding their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficients of the two like terms are 2 and 4.
To combine the like terms, we add their coefficients:
2m^2 + 4m^2 = 6m^2
So, the first two terms in the given expression can be combined as 6m^2.
Step 3: Simplify the Expression
Now that we have combined the like terms, we can simplify the expression by combining the remaining terms. The remaining terms are -m and 8m.
We can combine these terms by adding their coefficients:
-m + 8m = 7m
So, the simplified expression is:
6m^2 + 7m
Conclusion
In this article, we have simplified the given expression by combining like terms. We identified the like terms, combined them by adding their coefficients, and simplified the expression. This process is essential in algebra and is used to simplify complex expressions.
Final Answer
The final answer is:
6m^2 + 7m
Tips and Tricks
- When simplifying algebraic expressions, it is essential to identify like terms and combine them by adding their coefficients.
- Make sure to check your work by plugging in values for the variables and simplifying the expression.
- Practice simplifying algebraic expressions to become more comfortable with the process.
Common Mistakes
- Failing to identify like terms and combine them.
- Adding or subtracting coefficients incorrectly.
- Not checking work by plugging in values for the variables.
Real-World Applications
Simplifying algebraic expressions has many real-world applications, including:
- Physics: Simplifying expressions is essential in physics to solve problems involving motion, energy, and forces.
- Engineering: Simplifying expressions is used in engineering to design and optimize systems.
- Computer Science: Simplifying expressions is used in computer science to optimize algorithms and data structures.
Conclusion
Introduction
In our previous article, we discussed how to simplify algebraic expressions by combining like terms. In this article, we will provide a Q&A guide to help you understand the process better.
Q: What are like terms?
A: Like terms are algebraic expressions that have the same variable raised to the same power. In other words, they are terms that have the same base and exponent.
Q: How do I identify like terms?
A: To identify like terms, look for terms that have the same variable raised to the same power. For example, 2m^2 and 4m^2 are like terms because they both have the variable m raised to the power of 2.
Q: How do I combine like terms?
A: To combine like terms, add their coefficients. The coefficient of a term is the number that is multiplied by the variable. For example, to combine 2m^2 and 4m^2, we add their coefficients: 2 + 4 = 6. So, the combined term is 6m^2.
Q: What if I have multiple like terms?
A: If you have multiple like terms, combine them one at a time. For example, if you have 2m^2, 4m^2, and 6m^2, you would first combine 2m^2 and 4m^2 to get 6m^2, and then combine 6m^2 and 6m^2 to get 12m^2.
Q: Can I combine terms with different variables?
A: No, you cannot combine terms with different variables. For example, 2m^2 and 3n^2 are not like terms because they have different variables (m and n).
Q: What if I have a term with a negative coefficient?
A: If you have a term with a negative coefficient, you can combine it with other like terms as usual. For example, if you have -2m^2 and 4m^2, you would combine them to get 2m^2.
Q: Can I simplify expressions with fractions?
A: Yes, you can simplify expressions with fractions by combining like terms. For example, if you have 2/3m^2 and 4/3m^2, you would combine them to get 6/3m^2, which simplifies to 2m^2.
Q: What if I have an expression with multiple variables?
A: If you have an expression with multiple variables, you can simplify it by combining like terms. For example, if you have 2m^2n and 4m^2n, you would combine them to get 6m^2n.
Q: Can I use a calculator to simplify expressions?
A: Yes, you can use a calculator to simplify expressions. However, it's always a good idea to check your work by plugging in values for the variables and simplifying the expression.
Conclusion
In conclusion, simplifying algebraic expressions is an essential skill in mathematics. By understanding like terms and combining them by adding their coefficients, you can simplify complex expressions and solve problems in various fields. Practice simplifying algebraic expressions to become more comfortable with the process and to apply it in real-world scenarios.
Tips and Tricks
- Make sure to check your work by plugging in values for the variables and simplifying the expression.
- Practice simplifying algebraic expressions to become more comfortable with the process.
- Use a calculator to simplify expressions, but always check your work.
Common Mistakes
- Failing to identify like terms and combine them.
- Adding or subtracting coefficients incorrectly.
- Not checking work by plugging in values for the variables.
Real-World Applications
Simplifying algebraic expressions has many real-world applications, including:
- Physics: Simplifying expressions is essential in physics to solve problems involving motion, energy, and forces.
- Engineering: Simplifying expressions is used in engineering to design and optimize systems.
- Computer Science: Simplifying expressions is used in computer science to optimize algorithms and data structures.