What Is The Simplest Form Of This Expression?$-x(4x^2 - 6x + 1$\]A. $-4x^3 - 6x^2 - X$ B. $-4x^3 + 6x^2 - X$ C. $-4x^3 - 6x + 1$ D. $-4x^3 + 5x$

Understanding the Expression

The given expression is $-x(4x^2 - 6x + 1)$. To find the simplest form 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.

Applying the Distributive Property

To apply the distributive property, we multiply the term $-x$ with each term inside the parentheses: $-x(4x^2)$, $-x(-6x)$, and $-x(1)$.

Multiplying the Terms

Multiplying the terms, we get:

• $-x(4x^2) = -4x^3$
• $-x(-6x) = 6x^2$
• $-x(1) = -x$

Combining the Terms

Now, we combine the terms we obtained in the previous step: $-4x^3 + 6x^2 - x$.

Conclusion

Therefore, the simplest form of the expression $-x(4x^2 - 6x + 1)$ is $-4x^3 + 6x^2 - x$.

Comparison with the Options

Comparing the result we obtained with the options provided, we can see that the correct answer is option B: $-4x^3 + 6x^2 - x$.

Final Answer

The final answer is $-4x^3 + 6x^2 - x$.

Understanding the Expression

The given expression is $-x(4x^2 - 6x + 1)$. To find the simplest form 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.

Q&A Session

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 we can multiply a single term with multiple terms inside the parentheses.

Q: How do we apply the distributive property to the given expression?

A: To apply the distributive property, we multiply the term $-x$ with each term inside the parentheses: $-x(4x^2)$, $-x(-6x)$, and $-x(1)$.

Q: What are the results of multiplying the terms?

A: Multiplying the terms, we get:

• $-x(4x^2) = -4x^3$
• $-x(-6x) = 6x^2$
• $-x(1) = -x$

Q: How do we combine the terms?

A: Now, we combine the terms we obtained in the previous step: $-4x^3 + 6x^2 - x$.

Q: What is the simplest form of the expression?

A: Therefore, the simplest form of the expression $-x(4x^2 - 6x + 1)$ is $-4x^3 + 6x^2 - x$.

Q: How do we compare the result with the options provided?

A: Comparing the result we obtained with the options provided, we can see that the correct answer is option B: $-4x^3 + 6x^2 - x$.

Q: What is the final answer?

A: The final answer is $-4x^3 + 6x^2 - x$.

Common Mistakes

• Not applying the distributive property correctly
• Not multiplying the terms correctly
• Not combining the terms correctly

Tips and Tricks

• Make sure to apply the distributive property correctly
• Multiply the terms carefully
• Combine the terms correctly

Conclusion

In conclusion, the simplest form of the expression $-x(4x^2 - 6x + 1)$ is $-4x^3 + 6x^2 - x$. We hope this Q&A session has helped you understand the concept better.

Final Answer

The final answer is $-4x^3 + 6x^2 - x$.