What Is The Missing Coefficient In The Expression?$\[ \left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right) = \square X^2 + 6y^2 + 6x \\]A. 4 B. 8 C. 10 D. 22

Introduction

In algebra, a coefficient is a number that is multiplied by a variable. In the given expression, we have a quadratic equation with variables x and y. The expression is a combination of two quadratic expressions, and we need to find the missing coefficient in the resulting expression. In this article, we will analyze the given expression, simplify it, and find the missing coefficient.

Understanding the Expression

The given expression is:

$\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right) = \square x^2 + 6y^2 + 6x$

We can start by simplifying the expression by combining like terms. The like terms are the terms with the same variable and exponent.

Simplifying the Expression

To simplify the expression, we need to combine the like terms. We can start by combining the x terms:

$8x - 2x = 6x$

Now, we can rewrite the expression as:

$\left(15x^2 + 11y^2 + 6x\right) - \left(7x^2 + 5y^2\right) = \square x^2 + 6y^2 + 6x$

Next, we can combine the x^2 terms:

$15x^2 - 7x^2 = 8x^2$

Now, we can rewrite the expression as:

$8x^2 + 11y^2 - 5y^2 + 6x = \square x^2 + 6y^2 + 6x$

Combining Like Terms

We can combine the y terms:

$11y^2 - 5y^2 = 6y^2$

Now, we can rewrite the expression as:

$8x^2 + 6y^2 + 6x = \square x^2 + 6y^2 + 6x$

Finding the Missing Coefficient

The missing coefficient is the number that is multiplied by the x^2 term. We can see that the x^2 term is 8x^2. Therefore, the missing coefficient is 8.

Conclusion

In this article, we analyzed the given expression, simplified it, and found the missing coefficient. The missing coefficient is 8. We can verify this by plugging in the value of the missing coefficient into the expression and simplifying it.

Answer

The correct answer is B. 8.

Discussion

This problem is a great example of how to simplify an expression by combining like terms. It also shows how to find the missing coefficient in an expression. The problem is a good exercise for students who are learning algebra.

Tips and Tricks

• When simplifying an expression, make sure to combine like terms.
• When finding the missing coefficient, make sure to identify the variable and exponent.
• When plugging in the value of the missing coefficient, make sure to simplify the expression.

Related Problems

• Find the missing coefficient in the expression: $\left(3x^2 + 2y^2 + 4x\right) - \left(x^2 + y^2 + 2x\right) = \square x^2 + 3y^2 + 2x$
• Simplify the expression: $\left(2x^2 + 3y^2 + 4x\right) + \left(x^2 + 2y^2 + 3x\right)$
• Find the missing coefficient in the expression: $\left(5x^2 + 3y^2 + 2x\right) - \left(2x^2 + y^2 + x\right) = \square x^2 + 2y^2 + x$
  Frequently Asked Questions (FAQs) =====================================

Q: What is the missing coefficient in the expression $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right) = \square x^2 + 6y^2 + 6x$?

A: The missing coefficient is 8.

Q: How do I simplify the expression $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right)$?

A: To simplify the expression, you need to combine like terms. The like terms are the terms with the same variable and exponent. You can start by combining the x terms and then combine the x^2 terms.

Q: What is the first step in simplifying the expression $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right)$?

A: The first step is to combine the x terms. You can do this by subtracting the x terms in the second expression from the x terms in the first expression.

Q: How do I find the missing coefficient in the expression $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right)$?

A: To find the missing coefficient, you need to identify the variable and exponent of the term that is missing. In this case, the missing term is $8x^2$. Therefore, the missing coefficient is 8.

Q: What is the final expression after simplifying $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right)$?

A: The final expression is $8x^2 + 6y^2 + 6x$.

Q: How do I verify the missing coefficient in the expression $\left(15x^2 + 11y^2 + 8x\right) - \left(7x^2 + 5y^2 + 2x\right)$?

A: To verify the missing coefficient, you can plug in the value of the missing coefficient into the expression and simplify it. If the simplified expression matches the original expression, then the missing coefficient is correct.

Q: What is the importance of combining like terms in simplifying expressions?

A: Combining like terms is an important step in simplifying expressions. It helps to reduce the complexity of the expression and makes it easier to solve.

Q: How do I identify like terms in an expression?

A: Like terms are terms with the same variable and exponent. For example, in the expression $2x^2 + 3x^2$, the like terms are $2x^2$ and $3x^2$.

Q: What is the difference between a coefficient and a constant?

A: A coefficient is a number that is multiplied by a variable, while a constant is a number that is not multiplied by a variable.

Q: How do I find the missing coefficient in an expression with multiple variables?

A: To find the missing coefficient in an expression with multiple variables, you need to identify the variable and exponent of the term that is missing. Then, you can plug in the value of the missing coefficient into the expression and simplify it to verify the answer.