Simplify The Expression By Combining Like Terms.${ 3m + 9m }$ { 3m + 9m = \square \}

Introduction

In mathematics, combining like terms is a fundamental concept that helps simplify expressions and make them easier to work with. It involves adding or subtracting terms that have the same variable and exponent. In this article, we will explore how to simplify the expression by combining like terms, using the given example: $3m + 9m$.

Understanding Like Terms

Like terms are terms that have the same variable and exponent. For example, $3m$ and $9m$ are like terms because they both have the variable $m$ and the exponent is not specified, implying it is to the power of 1. To combine like terms, we need to add or subtract their coefficients.

Combining Like Terms

To combine like terms, we need to follow these steps:

1. Identify the like terms: In the given expression $3m + 9m$, we can see that both terms have the variable $m$ and the exponent is not specified.
2. Add or subtract the coefficients: The coefficients of the like terms are 3 and 9. To combine them, we add their values: $3 + 9 = 12$.
3. Write the combined term: The combined term is $12m$.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by writing it in its simplest form: $12m$.

Example

Let's consider another example: $2x + 5x + 3x$. To simplify this expression, we need to combine the like terms:

1. Identify the like terms: The like terms are $2x$, $5x$, and $3x$.
2. Add or subtract the coefficients: The coefficients of the like terms are 2, 5, and 3. To combine them, we add their values: $2 + 5 + 3 = 10$.
3. Write the combined term: The combined term is $10x$.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by writing it in its simplest form: $10x$.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions by combining like terms:

• Look for like terms: When simplifying an expression, look for like terms that can be combined.
• Add or subtract coefficients: When combining like terms, add or subtract their coefficients.
• Write the combined term: Write the combined term in its simplest form.

Conclusion

Simplifying expressions by combining like terms is an essential concept in mathematics. By following the steps outlined in this article, you can simplify expressions and make them easier to work with. Remember to look for like terms, add or subtract coefficients, and write the combined term in its simplest form.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying expressions by combining like terms:

• Not identifying like terms: Failing to identify like terms can lead to incorrect simplifications.
• Not adding or subtracting coefficients: Failing to add or subtract coefficients can lead to incorrect simplifications.
• Not writing the combined term: Failing to write the combined term in its simplest form can lead to incorrect simplifications.

Real-World Applications

Simplifying expressions by combining like terms has many real-world applications, including:

• Algebra: Simplifying expressions by combining like terms is essential in algebra, where it is used to solve equations and inequalities.
• Calculus: Simplifying expressions by combining like terms is used in calculus to find derivatives and integrals.
• Physics: Simplifying expressions by combining like terms is used in physics to solve problems involving motion and energy.

Final Thoughts

Introduction

In our previous article, we explored how to simplify expressions by combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions by combining like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $3m$ and $9m$ are like terms because they both have the variable $m$ and the exponent is not specified.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable and exponent. For example, in the expression $2x + 5x + 3x$, the like terms are $2x$, $5x$, and $3x$ because they all have the variable $x$ and the exponent is not specified.

Q: How do I combine like terms?

A: To combine like terms, add or subtract their coefficients. For example, in the expression $2x + 5x + 3x$, the coefficients are 2, 5, and 3. To combine them, add their values: $2 + 5 + 3 = 10$. The combined term is $10x$.

Q: What if I have a negative coefficient?

A: If you have a negative coefficient, you can still combine like terms. For example, in the expression $-2x + 5x + 3x$, the coefficients are -2, 5, and 3. To combine them, add their values: $-2 + 5 + 3 = 6$. The combined term is $6x$.

Q: Can I combine like terms with different variables?

A: No, you cannot combine like terms with different variables. For example, in the expression $2x + 5y + 3z$, you cannot combine the terms $2x$ and $5y$ because they have different variables.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, combine the like terms one at a time. For example, in the expression $2x + 5x + 3x + 4x$, first combine the like terms $2x$ and $5x$ to get $7x$. Then, combine the like terms $7x$ and $3x$ to get $10x$. Finally, combine the like terms $10x$ and $4x$ to get $14x$.

Q: Can I simplify an expression with variables and constants?

A: Yes, you can simplify an expression with variables and constants by combining like terms. For example, in the expression $2x + 5 + 3x$, first combine the like terms $2x$ and $3x$ to get $5x$. Then, combine the constant terms $5$ and $0$ (since there is no constant term in the expression) to get $5$. The simplified expression is $5x + 5$.

Q: How do I check my work when simplifying an expression?

A: To check your work when simplifying an expression, plug in a value for the variable and evaluate the expression. For example, if you simplify the expression $2x + 5x + 3x$ to get $10x$, plug in a value for $x$, such as $x = 1$, and evaluate the expression: $2(1) + 5(1) + 3(1) = 10$. If the result is correct, then your simplification is correct.

Conclusion

Simplifying expressions by combining like terms is an essential concept in mathematics. By following the steps outlined in this article, you can simplify expressions and make them easier to work with. Remember to look for like terms, add or subtract coefficients, and write the combined term in its simplest form.