Simplify The Expression:$3m^2 - 2m + 4m$

Feb 26, 2025 by ADMIN 41 views

Introduction

In algebra, simplifying expressions is a crucial step in solving equations and inequalities. It involves combining like terms to reduce the complexity of an expression, making it easier to work with. In this article, we will focus on simplifying the expression $3m^2 - 2m + 4m$ . We will use the rules of algebra to combine like terms and arrive at the simplified expression.

Understanding Like Terms

Before we can simplify the expression, we need to understand what like terms are. Like terms are terms that have the same variable raised to the same power. In the expression $3m^2 - 2m + 4m$ , the terms $-2m$ and $4m$ are like terms because they both have the variable $m$ raised to the power of 1.

Combining Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract their coefficients. The coefficient of a term is the number that is multiplied by the variable. In the expression $3m^2 - 2m + 4m$ , the coefficient of the term $-2m$ is -2, and the coefficient of the term $4m$ is 4.

Simplifying the Expression

To simplify the expression, we will combine the like terms $-2m$ and $4m$ . We do this by adding their coefficients:

-2m + 4m = (4 - 2)m = 2m

Now that we have combined the like terms, we can rewrite the expression as:

3m^2 + 2m

Final Answer

The simplified expression is $3m^2 + 2m$ .

Conclusion

In this article, we simplified the expression $3m^2 - 2m + 4m$ by combining like terms. We identified the like terms, added their coefficients, and arrived at the simplified expression. This process is an essential step in solving equations and inequalities in algebra.

Tips and Tricks

When simplifying expressions, always look for like terms.
Combine like terms by adding or subtracting their coefficients.
Use the distributive property to expand expressions and simplify them.

Common Mistakes

Failing to identify like terms.
Not combining like terms correctly.
Not using the distributive property to expand expressions.

Real-World Applications

Simplifying expressions is an essential skill in many real-world applications, including:

Physics: Simplifying expressions is crucial in physics to solve equations and inequalities that describe the motion of objects.
Engineering: Simplifying expressions is essential in engineering to design and optimize systems.
Computer Science: Simplifying expressions is a key step in computer science to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental concept in algebra that has many real-world applications. By understanding like terms and combining them correctly, we can simplify expressions and solve equations and inequalities. Remember to always look for like terms, combine them correctly, and use the distributive property to expand expressions.

Additional Resources

Khan Academy: Simplifying Expressions
Mathway: Simplifying Expressions
Wolfram Alpha: Simplifying Expressions

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: Combine like terms by adding or subtracting their coefficients.
Q: What is the distributive property? A: The distributive property is a rule that allows us to expand expressions by multiplying each term by a factor.

Introduction

In our previous article, we simplified the expression $3m^2 - 2m + 4m$ by combining like terms. In this article, we will answer some frequently asked questions about simplifying expressions.

Q&A

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 $3m^2 - 2m + 4m$ , the terms $-2m$ and $4m$ are like terms because they both have the variable $m$ raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you add or subtract their coefficients. The coefficient of a term is the number that is multiplied by the variable. For example, in the expression $3m^2 - 2m + 4m$ , the coefficient of the term $-2m$ is -2, and the coefficient of the term $4m$ is 4. To combine these terms, you add their coefficients:

-2m + 4m = (4 - 2)m = 2m

Q: What is the distributive property?

A: The distributive property is a rule that allows us to expand expressions by multiplying each term by a factor. For example, if we have the expression $3(m + 2)$ , we can use the distributive property to expand it as:

3(m + 2) = 3m + 6

Q: How do I simplify an expression with multiple variables?

A: To simplify an expression with multiple variables, you need to identify the like terms and combine them. For example, if we have the expression $2x^2 + 3y^2 - 4x + 5y$ , we can identify the like terms as $2x^2$ and $-4x$ , and $3y^2$ and $5y$ . We can then combine these terms as:

2x^2 - 4x + 3y^2 + 5y

Q: Can I simplify an expression with a negative coefficient?

A: Yes, you can simplify an expression with a negative coefficient. For example, if we have the expression $-2x^2 + 3x - 4$ , we can simplify it by combining the like terms:

-2x^2 + 3x - 4 = -2x^2 + 3x - 4

Q: How do I simplify an expression with a fraction?

A: To simplify an expression with a fraction, you need to multiply the numerator and denominator by the same factor to eliminate the fraction. For example, if we have the expression $\frac{2x^2}{3} + \frac{4x}{3}$ , we can simplify it by multiplying the numerator and denominator by 3:

\frac{2x^2}{3} + \frac{4x}{3} = \frac{6x^2}{9} + \frac{12x}{9} = \frac{2x^2 + 4x}{3}

Q: Can I simplify an expression with a variable in the denominator?

A: No, you cannot simplify an expression with a variable in the denominator. For example, if we have the expression $\frac{2x^2}{x}$ , we cannot simplify it because the variable $x$ is in the denominator.