Simplify The Expression:${ M(3m - 2) + 2m }$

Mar 11, 2025 by ADMIN 46 views

**Simplify the Expression: A Step-by-Step Guide**

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will simplify the given expression: $m(3m - 2) + 2m$ . We will break down the expression into smaller parts, apply the distributive property, and combine like terms to simplify it.

Understanding the Expression

The given expression is $m(3m - 2) + 2m$ . This expression consists of two terms: $m(3m - 2)$ and $2m$ . The first term is a product of two expressions, while the second term is a single expression.

Step 1: Apply the Distributive Property

To simplify the expression, we will start by applying the distributive property to the first term: $m(3m - 2)$ . The distributive property states that for any real numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . We can apply this property to the first term by multiplying $m$ with each term inside the parentheses.

m(3m - 2) = m(3m) - m(2)

Step 2: Simplify the First Term

Now that we have applied the distributive property, we can simplify the first term by multiplying $m$ with each term inside the parentheses.

m(3m) = 3m^2
m(2) = 2m

So, the first term simplifies to $3m^2 - 2m$ .

Step 3: Combine Like Terms

Now that we have simplified the first term, we can combine like terms with the second term: $2m$ . Like terms are terms that have the same variable raised to the same power.

3m^2 - 2m + 2m

We can combine the two $2m$ terms to get:

3m^2

Step 4: Final Simplification

The expression $m(3m - 2) + 2m$ simplifies to $3m^2$ .

Conclusion

In this article, we simplified the expression $m(3m - 2) + 2m$ by applying the distributive property, simplifying the first term, combining like terms, and finally simplifying the expression. We hope this step-by-step guide has helped you understand how to simplify expressions in algebra.

Tips and Tricks

When simplifying expressions, always start by applying the distributive property to any product of expressions.
Combine like terms by adding or subtracting the coefficients of the same variable raised to the same power.
Always check your work by plugging in simple values for the variables to ensure that the expression simplifies correctly.

Common Mistakes

Failing to apply the distributive property to products of expressions.
Not combining like terms correctly.
Not checking work by plugging in simple values for the variables.

Real-World Applications

Simplifying expressions is a crucial skill in algebra that has many real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In economics, we use algebraic expressions to model the behavior of markets. In computer science, we use algebraic expressions to write algorithms and programs.

Final Thoughts

Introduction

In our previous article, we simplified the expression $m(3m - 2) + 2m$ by applying the distributive property, simplifying the first term, combining like terms, and finally simplifying the expression. In this article, we will answer some common questions that students often have when simplifying expressions.

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that states that for any real numbers $a$ , $b$ , and $c$ , $a(b + c) = ab + ac$ . This means that we can multiply a single term by each term inside the parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, simply multiply the single term by each term inside the parentheses. For example, if we have the expression $m(3m - 2)$ , we can apply the distributive property by multiplying $m$ with each term inside the parentheses: $m(3m) - m(2)$ .

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2m$ 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, simply add or subtract the coefficients of the same variable raised to the same power. For example, if we have the expression $3m^2 - 2m + 2m$ , we can combine the two $2m$ terms by adding their coefficients: $3m^2 + 0m$ .

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

Failing to apply the distributive property to products of expressions.
Not combining like terms correctly.
Not checking work by plugging in simple values for the variables.

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, simply plug in simple values for the variables and see if the expression simplifies correctly. For example, if we have the expression $m(3m - 2) + 2m$ , we can plug in $m = 1$ and see if the expression simplifies to $3(1) - 2 + 2(1)$ .

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions has many real-world applications, including:

Physics: Algebraic expressions are used to describe the motion of objects.
Economics: Algebraic expressions are used to model the behavior of markets.
Computer Science: Algebraic expressions are used to write algorithms and programs.

Q: How can I practice simplifying expressions?

A: There are many ways to practice simplifying expressions, including:

Working through practice problems in a textbook or online resource.
Creating your own practice problems and simplifying them.
Using online tools or apps to generate practice problems and simplify them.

Conclusion

Simplifying expressions is a fundamental skill in algebra that requires practice and patience. By following the steps outlined in this article and practicing regularly, you can become proficient in simplifying expressions and be able to tackle even the most complex algebraic problems. Remember to always apply the distributive property, combine like terms, and check your work by plugging in simple values for the variables.