Distribute $10x(-x-1)$.
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Understanding the Concept of Distribution
In algebra, distributing a term involves multiplying the term by each of the terms inside the parentheses. This process is essential in simplifying expressions and solving equations. When distributing a term, we multiply the term by each of the terms inside the parentheses, and then combine like terms.
Distributing the Term $10x(-x-1)$
To distribute the term $10x$ into the expression $(-x-1)$, we need to multiply $10x$ by each of the terms inside the parentheses. This involves multiplying $10x$ by $-x$ and then multiplying $10x$ by $-1$.
Multiplying $10x$ by $-x$
When multiplying $10x$ by $-x$, we need to multiply the coefficients and the variables separately. The coefficient of $10x$ is $10$, and the coefficient of $-x$ is $-1$. Multiplying the coefficients gives us $-10$, and multiplying the variables gives us $x^2$.
Multiplying $10x$ by $-1$
When multiplying $10x$ by $-1$, we need to multiply the coefficients and the variables separately. The coefficient of $10x$ is $10$, and the coefficient of $-1$ is $-1$. Multiplying the coefficients gives us $-10$, and multiplying the variables gives us $-x$.
Combining Like Terms
After distributing the term $10x$ into the expression $(-x-1)$, we get $-10x^2 - 10x$. This expression can be simplified by combining like terms. The like terms in this expression are $-10x^2$ and $-10x$.
Combining $-10x^2$ and $-10x$
To combine $-10x^2$ and $-10x$, we need to add the coefficients of the like terms. The coefficient of $-10x^2$ is $-10$, and the coefficient of $-10x$ is $-10$. Adding the coefficients gives us $-20$.
Final Answer
The final answer to distributing the term $10x(-x-1)$ is $-10x^2 - 10x$.
Example Use Case
Distributing the term $10x(-x-1)$ is an essential step in solving equations and simplifying expressions. For example, consider the equation $10x(-x-1) = 5$. To solve this equation, we need to distribute the term $10x$ into the expression $(-x-1)$, and then combine like terms.
Step 1: Distribute the Term
To distribute the term $10x$ into the expression $(-x-1)$, we need to multiply $10x$ by each of the terms inside the parentheses. This involves multiplying $10x$ by $-x$ and then multiplying $10x$ by $-1$.
Step 2: Combine Like Terms
After distributing the term $10x$ into the expression $(-x-1)$, we get $-10x^2 - 10x$. This expression can be simplified by combining like terms. The like terms in this expression are $-10x^2$ and $-10x$.
Step 3: Solve the Equation
To solve the equation $10x(-x-1) = 5$, we need to set the expression $-10x^2 - 10x$ equal to $5$, and then solve for $x$. This involves adding $10x^2 + 10x$ to both sides of the equation, and then factoring the left-hand side of the equation.
Conclusion
Distributing the term $10x(-x-1)$ is an essential step in solving equations and simplifying expressions. By following the steps outlined in this article, we can distribute the term $10x$ into the expression $(-x-1)$, and then combine like terms to simplify the expression. This process is essential in solving equations and simplifying expressions, and is a fundamental concept in algebra.
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Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about distributing the term $10x(-x-1)$.
Q: What is distribution in algebra?
A: Distribution in algebra involves multiplying a term by each of the terms inside the parentheses. This process is essential in simplifying expressions and solving equations.
Q: How do I distribute the term $10x$ into the expression $(-x-1)$?
A: To distribute the term $10x$ into the expression $(-x-1)$, you need to multiply $10x$ by each of the terms inside the parentheses. This involves multiplying $10x$ by $-x$ and then multiplying $10x$ by $-1$.
Q: What is the final answer to distributing the term $10x(-x-1)$?
A: The final answer to distributing the term $10x(-x-1)$ is $-10x^2 - 10x$.
Q: Can I simplify the expression $-10x^2 - 10x$?
A: Yes, you can simplify the expression $-10x^2 - 10x$ by combining like terms. The like terms in this expression are $-10x^2$ and $-10x$.
Q: How do I combine like terms in the expression $-10x^2 - 10x$?
A: To combine like terms in the expression $-10x^2 - 10x$, you need to add the coefficients of the like terms. The coefficient of $-10x^2$ is $-10$, and the coefficient of $-10x$ is $-10$. Adding the coefficients gives us $-20$.
Q: What is the final simplified expression?
A: The final simplified expression is $-20x^2 - 20x$.
Q: Can I use this concept to solve equations?
A: Yes, you can use this concept to solve equations. For example, consider the equation $10x(-x-1) = 5$. To solve this equation, you need to distribute the term $10x$ into the expression $(-x-1)$, and then combine like terms.
Q: How do I solve the equation $10x(-x-1) = 5$?
A: To solve the equation $10x(-x-1) = 5$, you need to set the expression $-10x^2 - 10x$ equal to $5$, and then solve for $x$. This involves adding $10x^2 + 10x$ to both sides of the equation, and then factoring the left-hand side of the equation.
Q: What is the final solution to the equation $10x(-x-1) = 5$?
A: The final solution to the equation $10x(-x-1) = 5$ is $x = -\frac{1}{2}$.
Conclusion
Distributing the term $10x(-x-1)$ is an essential step in solving equations and simplifying expressions. By following the steps outlined in this article, we can distribute the term $10x$ into the expression $(-x-1)$, and then combine like terms to simplify the expression. This process is essential in solving equations and simplifying expressions, and is a fundamental concept in algebra.
Additional Resources
If you need additional help with distributing the term $10x(-x-1)$, you can try the following resources:
- Khan Academy: Distributing Terms in Algebra
- Mathway: Distributing Terms in Algebra
- Algebra.com: Distributing Terms in Algebra
These resources provide additional examples and practice problems to help you master the concept of distributing terms in algebra.