What Is The Product Of The Expression?${ -9x(5 - 2x) }$A. ${ 18x^2 - 45x\$} B. { -18x^2 - 45x$}$C. { -18x - 45x$}$D. ${ 18x - 45x\$}

Understanding the Expression

The given expression is $-9x(5 - 2x)$. 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 a single term inside the parentheses, $5 - 2x$, which we need to multiply by the factor $-9x$.

Applying the Distributive Property

To find the product, we will multiply each term inside the parentheses by $-9x$. This means we will multiply $5$ by $-9x$ and $-2x$ by $-9x$. The distributive property allows us to break down the multiplication into two separate steps.

Multiplying $5$ by $-9x$

When we multiply $5$ by $-9x$, we get $-45x$. This is because multiplying a positive number by a negative number results in a negative number, and multiplying a number by a variable (in this case, $x$) results in the variable being multiplied by the number.

Multiplying $-2x$ by $-9x$

When we multiply $-2x$ by $-9x$, we get $18x^2$. This is because multiplying two negative numbers results in a positive number, and multiplying two variables (in this case, $x$ and $x$) results in the variables being multiplied together, which is equivalent to squaring the variable.

Combining the Terms

Now that we have multiplied each term inside the parentheses by $-9x$, we can combine the two resulting terms to get the final product. The product of the expression $-9x(5 - 2x)$ is therefore $-45x + 18x^2$.

Evaluating the Answer Choices

Now that we have found the product of the expression, we can evaluate the answer choices to see which one matches our result.

• A. $18x^2 - 45x$: This answer choice is incorrect because it has the terms in the opposite order of what we found.
• B. $-18x^2 - 45x$: This answer choice is incorrect because it has a negative sign in front of both terms, whereas our result had a negative sign only in front of the $45x$ term.
• C. $-18x - 45x$: This answer choice is incorrect because it has the terms $-18x$ and $-45x$, whereas our result had the terms $-45x$ and $18x^2$.
• D. $18x - 45x$: This answer choice is incorrect because it has the terms $18x$ and $-45x$, whereas our result had the terms $-45x$ and $18x^2$.

Conclusion

The correct answer is A. $18x^2 - 45x$. However, this is not the correct answer because the expression is $-9x(5 - 2x)$ and the correct answer is $-9x(5 - 2x) = -9x(5) + (-9x)(-2x) = -45x + 18x^2$.

Frequently Asked Questions

Q: What is the product of the expression $-9x(5 - 2x)$?

A: The product of the expression $-9x(5 - 2x)$ is $-45x + 18x^2$. This is found by applying the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Q: Why is the product of the expression $-9x(5 - 2x)$ equal to $-45x + 18x^2$?

A: The product of the expression $-9x(5 - 2x)$ is equal to $-45x + 18x^2$ because we multiplied each term inside the parentheses by $-9x$. This means we multiplied $5$ by $-9x$ to get $-45x$, and we multiplied $-2x$ by $-9x$ to get $18x^2$.

Q: What is the distributive property, and how is it used to find the product of the expression $-9x(5 - 2x)$?

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 property is used to find the product of the expression $-9x(5 - 2x)$ by multiplying each term inside the parentheses by $-9x$.

Q: How do I apply the distributive property to find the product of the expression $-9x(5 - 2x)$?

A: To apply the distributive property, you need to multiply each term inside the parentheses by the factor outside the parentheses. In this case, you need to multiply $5$ by $-9x$ and $-2x$ by $-9x$. This will give you the product of the expression $-9x(5 - 2x)$.

Q: What are the answer choices for the product of the expression $-9x(5 - 2x)$?

A: The answer choices for the product of the expression $-9x(5 - 2x)$ are:

• A. $18x^2 - 45x$
• B. $-18x^2 - 45x$
• C. $-18x - 45x$
• D. $18x - 45x$

Q: Which answer choice is correct for the product of the expression $-9x(5 - 2x)$?

A: The correct answer choice for the product of the expression $-9x(5 - 2x)$ is A. $18x^2 - 45x$. However, this is not the correct answer because the expression is $-9x(5 - 2x)$ and the correct answer is $-9x(5) + (-9x)(-2x) = -45x + 18x^2$.

Q: What is the final answer for the product of the expression $-9x(5 - 2x)$?

A: The final answer for the product of the expression $-9x(5 - 2x)$ is $-45x + 18x^2$.

Conclusion

The product of the expression $-9x(5 - 2x)$ is $-45x + 18x^2$. This is found by applying the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. The correct answer choice is A. $18x^2 - 45x$, but this is not the correct answer because the expression is $-9x(5 - 2x)$ and the correct answer is $-45x + 18x^2$.