Which Expression Is Equivalent To 7 M ( 3 M − 4 7m(3m-4 7 M ( 3 M − 4 ]?A. 21 M 2 − 28 M 21m^2 - 28m 21 M 2 − 28 M B. 10 M 2 − 3 M 10m^2 - 3m 10 M 2 − 3 M C. 10 M − 3 10m - 3 10 M − 3 D. 21 M 2 − 28 21m^2 - 28 21 M 2 − 28 E. 21 M 2 + 28 M 21m^2 + 28m 21 M 2 + 28 M

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Introduction

In algebra, we often encounter expressions that involve the multiplication of two or more terms. When we multiply expressions, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b+c) = ab + ac$. In this article, we will explore which expression is equivalent to $7m(3m-4)$.

Understanding the Distributive Property

The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. In the expression $7m(3m-4)$, we have a term $7m$ outside the parentheses and a term $3m-4$ inside the parentheses. To apply the distributive property, we need to multiply $7m$ with each term inside the parentheses.

Applying the Distributive Property

To apply the distributive property, we multiply $7m$ with $3m$ and $-4$ separately. This gives us:

$7m(3m-4) = 7m(3m) + 7m(-4)$

Simplifying the Expression

Now, we simplify each term separately. When we multiply $7m$ with $3m$, we get:

$7m(3m) = 21m^2$

When we multiply $7m$ with $-4$, we get:

$7m(-4) = -28m$

Combining the Terms

Now, we combine the two terms we obtained in the previous step:

$7m(3m-4) = 21m^2 - 28m$

Comparing with the Options

Now, we compare the expression we obtained with the options provided:

A. $21m^2 - 28m$ B. $10m^2 - 3m$ C. $10m - 3$ D. $21m^2 - 28$ E. $21m^2 + 28m$

Conclusion

Based on our analysis, we can see that the expression $7m(3m-4)$ is equivalent to option A, which is $21m^2 - 28m$. This is because we applied the distributive property and simplified the expression to obtain this result.

Final Answer

The final answer is A. $21m^2 - 28m$.

Frequently Asked Questions

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do we apply the distributive property?

A: To apply the distributive property, we multiply the term outside the parentheses with each term inside the parentheses.

Q: What is the final answer?

A: The final answer is A. $21m^2 - 28m$.

Additional Resources

For more information on the distributive property and algebra, you can refer to the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

Conclusion

In conclusion, we have explored which expression is equivalent to $7m(3m-4)$. We applied the distributive property and simplified the expression to obtain the final answer, which is A. $21m^2 - 28m$. We hope this article has provided you with a clear understanding of the distributive property and how to apply it in algebra.

Introduction

In our previous article, we explored which expression is equivalent to $7m(3m-4)$. We applied the distributive property and simplified the expression to obtain the final answer, which is A. $21m^2 - 28m$. In this article, we will answer some frequently asked questions related to algebra and the distributive property.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.

Q: How do we apply the distributive property?

A: To apply the distributive property, we multiply the term outside the parentheses with each term inside the parentheses.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. The commutative property, on the other hand, allows us to rearrange the order of terms in an expression without changing its value.

Q: Can we apply the distributive property to expressions with more than two terms?

A: Yes, we can apply the distributive property to expressions with more than two terms. For example, if we have the expression $a(b+c+d)$, we can apply the distributive property to get $ab + ac + ad$.

Q: How do we simplify expressions using the distributive property?

A: To simplify expressions using the distributive property, we need to multiply each term inside the parentheses with the term outside the parentheses and then combine like terms.

Q: What is the importance of the distributive property in algebra?

A: The distributive property is an essential concept in algebra that allows us to expand and simplify expressions. It is used extensively in algebraic manipulations, such as solving equations and inequalities.

Q: Can we apply the distributive property to expressions with variables and constants?

A: Yes, we can apply the distributive property to expressions with variables and constants. For example, if we have the expression $2x(3x+4)$, we can apply the distributive property to get $6x^2 + 8x$.

Q: How do we check if two expressions are equivalent using the distributive property?

A: To check if two expressions are equivalent using the distributive property, we need to apply the distributive property to each expression and then compare the results.

Q: What are some common mistakes to avoid when applying the distributive property?

A: Some common mistakes to avoid when applying the distributive property include:

• Forgetting to multiply each term inside the parentheses with the term outside the parentheses
• Not combining like terms
• Not checking if the expressions are equivalent

Conclusion

In conclusion, we have answered some frequently asked questions related to algebra and the distributive property. We hope this article has provided you with a clear understanding of the distributive property and how to apply it in algebra.

Additional Resources

For more information on the distributive property and algebra, you can refer to the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

Final Tips

• Practice applying the distributive property to different types of expressions
• Make sure to combine like terms when simplifying expressions
• Check if the expressions are equivalent by applying the distributive property to each expression

By following these tips and practicing regularly, you will become proficient in applying the distributive property and solving algebraic expressions.