Identifying the Missing Coefficient

Oct 13, 2025 by leolavanderia.com.br 30 views

Understanding the Problem

When dealing with algebraic expressions, it's essential to understand the concept of expanding and simplifying expressions. In this problem, we are given the expression ${-x-5}$ and asked to find the missing coefficient of the ${x}$ -term after it has been squared and simplified.

Expanding the Expression

To find the missing coefficient, we need to expand the given expression ${(-x-5)^2}$ . This can be done using the formula ${(a+b)^2 = a^2 + 2ab + b^2}$ , where ${a = -x}$ and ${b = -5}$ .

Applying the Formula

Using the formula, we can expand the expression as follows:

${(a+b)^2 = a^2 + 2ab + b^2}$ ${(-x-5)^2 = (-x)^2 + 2(-x)(-5) + (-5)^2}$ ${(-x-5)^2 = x^2 + 10x + 25}$

Identifying the Missing Coefficient

Now that we have expanded the expression, we can see that the ${x}$ -term is ${10x}$ . This means that the missing coefficient of the ${x}$ -term is ${10}$ .

Conclusion

In conclusion, the missing coefficient of the ${x}$ -term of the product ${(-x-5)^2}$ after it has been simplified is ${10}$ . This can be verified by expanding the expression and identifying the coefficient of the ${x}$ -term.

Frequently Asked Questions

What is the missing coefficient of the ${x}$ $x$ -term of the product ${(-x-5)^2}$ $(- x - 5)^{2}$ after it has been simplified?
- The missing coefficient of the ${x}$ -term is ${10}$ .
How do I expand the expression ${(-x-5)^2}$ $(- x - 5)^{2}$ ?
- Use the formula ${(a+b)^2 = a^2 + 2ab + b^2}$ , where ${a = -x}$ and ${b = -5}$ .
What is the coefficient of the ${x}$ $x$ -term in the expanded expression?
- The coefficient of the ${x}$ -term is ${10}$ .

Step-by-Step Solution

Expand the expression ${(-x-5)^2}$ using the formula ${(a+b)^2 = a^2 + 2ab + b^2}$ , where ${a = -x}$ and ${b = -5}$ .
Identify the ${x}$ -term in the expanded expression.
Determine the coefficient of the ${x}$ -term.

Common Mistakes

Failing to expand the expression correctly.
Not identifying the ${x}$ -term in the expanded expression.
Not determining the coefficient of the ${x}$ -term.

Real-World Applications

Algebraic expressions are used in various real-world applications, such as physics, engineering, and economics.
Understanding how to expand and simplify expressions is essential in solving problems in these fields.

Conclusion

Q&A: Missing Coefficient of the x-term

Q: What is the missing coefficient of the x-term of the product (-x-5)^2 after it has been simplified?

A: The missing coefficient of the x-term is 10.

Q: How do I expand the expression (-x-5)^2?

A: Use the formula (a+b)^2 = a^2 + 2ab + b^2, where a = -x and b = -5.

Q: What is the coefficient of the x-term in the expanded expression?

A: The coefficient of the x-term is 10.

Q: What is the formula for expanding a squared expression?

A: The formula for expanding a squared expression is (a+b)^2 = a^2 + 2ab + b^2.

Q: How do I identify the x-term in the expanded expression?

A: The x-term is the term that contains the variable x.

Q: What is the coefficient of the x-term in the expression x^2 + 10x + 25?

A: The coefficient of the x-term is 10.

Q: How do I determine the missing coefficient of the x-term?

A: To determine the missing coefficient of the x-term, expand the expression and identify the coefficient of the x-term.

Q: What is the real-world application of expanding and simplifying expressions?

A: Expanding and simplifying expressions is used in various real-world applications, such as physics, engineering, and economics.

Q: What are some common mistakes to avoid when expanding and simplifying expressions?

A: Some common mistakes to avoid include failing to expand the expression correctly, not identifying the x-term in the expanded expression, and not determining the coefficient of the x-term.

Q: How do I verify the missing coefficient of the x-term?

A: To verify the missing coefficient of the x-term, expand the expression and identify the coefficient of the x-term.

Additional Resources

For more information on expanding and simplifying expressions, visit the Khan Academy website.
For more information on algebraic expressions, visit the Mathway website.
For more information on real-world applications of algebraic expressions, visit the Wolfram Alpha website.

Conclusion

In conclusion, the missing coefficient of the x-term of the product (-x-5)^2 after it has been simplified is 10. This can be verified by expanding the expression and identifying the coefficient of the x-term. Remember to use the formula (a+b)^2 = a^2 + 2ab + b^2 to expand the expression, and to identify the x-term and its coefficient in the expanded expression.