What Is The Product Of The Expression?${3a(8a - 6b)}$A. ${24a^2 - 6b}$B. ${24a^2 - 6ab}$C. ${24a^2 - 18b^2}$D. ${24a^2 - 18ab}$

Understanding the Expression

The given expression is $3a(8a - 6b)$. To find the product of this expression, 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 case, we have $3a(8a - 6b)$, and we need to distribute the $3a$ to both terms inside the parentheses.

Distributing the Terms

To find the product, we will multiply the $3a$ with each term inside the parentheses. This means we will multiply $3a$ with $8a$ and $3a$ with $-6b$. The result will be the product of the expression.

Calculating the Product

Let's calculate the product step by step:

1. Multiply $3a$ with $8a$: $3a \times 8a = 24a^2$
2. Multiply $3a$ with $-6b$: $3a \times -6b = -18ab$

Combining the Terms

Now that we have multiplied each term inside the parentheses, we can combine the results to find the final product. The product of the expression $3a(8a - 6b)$ is $24a^2 - 18ab$.

Comparing with the Options

Let's compare our result with the options provided:

A. $24a^2 - 6b$ B. $24a^2 - 6ab$ C. $24a^2 - 18b^2$ D. $24a^2 - 18ab$

Our result matches option D, which is $24a^2 - 18ab$.

Conclusion

In conclusion, the product of the expression $3a(8a - 6b)$ is $24a^2 - 18ab$. This result can be obtained by applying the distributive property and multiplying each term inside the parentheses.

Frequently Asked Questions

• What is the distributive property? The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• How do I apply the distributive property? To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses.
• What is the product of the expression $3a(8a - 6b)$? The product of the expression $3a(8a - 6b)$ is $24a^2 - 18ab$.

Additional Resources

• Distributive Property: A comprehensive guide to the distributive property, including examples and practice problems.
• Algebra: A beginner's guide to algebra, including topics such as variables, expressions, and equations.
• Math Problems: A collection of math problems, including algebra, geometry, and trigonometry.

Final Answer

The final answer is $\boxed{24a^2 - 18ab}$.

Q&A: Product of the Expression $3a(8a - 6b)$

Q: What is the distributive property?

A: The distributive property is a mathematical concept that states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. This means that you can distribute a single term to multiple terms inside parentheses.

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. For example, in the expression $3a(8a - 6b)$, you would multiply $3a$ with $8a$ and $3a$ with $-6b$.

Q: What is the product of the expression $3a(8a - 6b)$?

A: The product of the expression $3a(8a - 6b)$ is $24a^2 - 18ab$. This result can be obtained by applying the distributive property and multiplying each term inside the parentheses.

Q: Why is the product of the expression $3a(8a - 6b)$ not $24a^2 - 6b$?

A: The product of the expression $3a(8a - 6b)$ is not $24a^2 - 6b$ because the term $-6b$ is multiplied by $3a$, resulting in $-18ab$, not $-6b$.

Q: Why is the product of the expression $3a(8a - 6b)$ not $24a^2 - 18b^2$?

A: The product of the expression $3a(8a - 6b)$ is not $24a^2 - 18b^2$ because the term $-6b$ is multiplied by $3a$, resulting in $-18ab$, not $-18b^2$.

Q: Why is the product of the expression $3a(8a - 6b)$ not $24a^2 - 6ab$?

A: The product of the expression $3a(8a - 6b)$ is not $24a^2 - 6ab$ because the term $-6b$ is multiplied by $3a$, resulting in $-18ab$, not $-6ab$.

Q: What is the final answer to the product of the expression $3a(8a - 6b)$?

A: The final answer to the product of the expression $3a(8a - 6b)$ is $\boxed{24a^2 - 18ab}$.

Additional Resources

• Distributive Property: A comprehensive guide to the distributive property, including examples and practice problems.
• Algebra: A beginner's guide to algebra, including topics such as variables, expressions, and equations.
• Math Problems: A collection of math problems, including algebra, geometry, and trigonometry.

Final Answer

The final answer is $\boxed{24a^2 - 18ab}$.