Subtract $x^2 + 8x$ From $-3x^2 - 3x - 7$.

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Introduction

In algebra, subtraction of polynomials is a fundamental operation that involves combining like terms to simplify the expression. When subtracting one polynomial from another, we need to be careful to combine like terms and simplify the resulting expression. In this article, we will learn how to subtract $x^2 + 8x$ from $-3x^2 - 3x - 7$.

Understanding the Problem

To subtract $x^2 + 8x$ from $-3x^2 - 3x - 7$, we need to first understand the concept of like terms. Like terms are terms that have the same variable raised to the same power. In this case, the like terms are the terms with the variable $x$ raised to the power of 2 and the terms with the variable $x$ raised to the power of 1.

Step 1: Identify the Like Terms

The like terms in the given expression are:

• $-3x^2$ and $x^2$
• $-3x$ and $8x$

Step 2: Combine the Like Terms

To combine the like terms, we need to subtract the coefficients of the like terms. The coefficients are the numbers that are multiplied by the variables.

• For the terms with $x^2$, the coefficient of $-3x^2$ is -3 and the coefficient of $x^2$ is 1. So, we subtract -3 from 1 to get -2.
• For the terms with $x$, the coefficient of $-3x$ is -3 and the coefficient of $8x$ is 8. So, we subtract -3 from 8 to get 11.

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by combining the constants.

• The constant term in the expression is -7.
• We can combine the constants by adding -7 to the result of the subtraction of the like terms.

Step 4: Write the Final Answer

The final answer is obtained by combining the results of the subtraction of the like terms and the constants.

$$-3x^2 - 3x - 7 - (x^2 + 8x) = -3x^2 - 3x - 7 - x^2 - 8x$$

$$= -3x^2 - x^2 - 3x - 8x - 7$$

$$= -4x^2 - 11x - 7$$

Conclusion

In this article, we learned how to subtract $x^2 + 8x$ from $-3x^2 - 3x - 7$. We identified the like terms, combined them, and simplified the expression to obtain the final answer. The final answer is $-4x^2 - 11x - 7$.

Example Problems

• Subtract $x^2 + 5x$ from $-2x^2 - 2x - 9$.
• Subtract $x^2 + 2x$ from $-4x^2 - 4x - 6$.

Tips and Tricks

• When subtracting polynomials, make sure to combine like terms and simplify the expression.
• Use the distributive property to expand the expression and combine like terms.
• Check your work by plugging in values for the variables and simplifying the expression.

Common Mistakes

• Failing to combine like terms.
• Failing to simplify the expression.
• Making errors when subtracting the coefficients of the like terms.

Real-World Applications

• Subtracting polynomials is used in many real-world applications, such as:
• Calculating the area of a rectangle.
• Finding the volume of a cube.
• Determining the cost of a product.

Final Thoughts

Subtracting polynomials is a fundamental operation in algebra that involves combining like terms to simplify the expression. By following the steps outlined in this article, you can learn how to subtract $x^2 + 8x$ from $-3x^2 - 3x - 7$ and apply this knowledge to real-world problems.

Introduction

In our previous article, we learned how to subtract $x^2 + 8x$ from $-3x^2 - 3x - 7$. In this article, we will answer some frequently asked questions about subtracting polynomials.

Q: What is the first step in subtracting polynomials?

A: The first step in subtracting polynomials is to identify the like terms. Like terms are terms that have the same variable raised to the same power.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $x^2 + 3x + 2$, the like terms are $x^2$ and $3x$.

Q: What is the next step after identifying like terms?

A: After identifying like terms, the next step is to combine them by subtracting the coefficients of the like terms.

Q: How do I combine like terms?

A: To combine like terms, subtract the coefficients of the like terms. For example, in the expression $-3x^2 + x^2$, the coefficients of the like terms are -3 and 1. So, we subtract -3 from 1 to get -2.

Q: What if I have multiple like terms?

A: If you have multiple like terms, combine them by subtracting the coefficients of the like terms. For example, in the expression $-3x^2 + x^2 + 2x^2$, the coefficients of the like terms are -3, 1, and 2. So, we subtract -3 from 1 and then add 2 to get 0.

Q: Can I simplify the expression after combining like terms?

A: Yes, you can simplify the expression after combining like terms. For example, in the expression $-3x^2 + x^2 + 2x^2$, we can simplify the expression by combining the constants.

Q: What is the final step in subtracting polynomials?

A: The final step in subtracting polynomials is to write the final answer.

Q: How do I write the final answer?

A: To write the final answer, combine the results of the subtraction of the like terms and the constants.

Q: Can I use a calculator to subtract polynomials?

A: Yes, you can use a calculator to subtract polynomials. However, it's always a good idea to check your work by plugging in values for the variables and simplifying the expression.

Q: What are some common mistakes to avoid when subtracting polynomials?

A: Some common mistakes to avoid when subtracting polynomials include:

• Failing to combine like terms.
• Failing to simplify the expression.
• Making errors when subtracting the coefficients of the like terms.

Q: How can I apply subtracting polynomials to real-world problems?

A: Subtracting polynomials can be applied to many real-world problems, such as:

• Calculating the area of a rectangle.
• Finding the volume of a cube.
• Determining the cost of a product.

Q: Can I use subtracting polynomials to solve equations?

A: Yes, you can use subtracting polynomials to solve equations. For example, if you have the equation $x^2 + 3x + 2 = 0$, you can subtract $x^2 + 2x$ from both sides to get $x + 2 = 0$.

Q: What are some tips and tricks for subtracting polynomials?

A: Some tips and tricks for subtracting polynomials include:

• Using the distributive property to expand the expression and combine like terms.
• Checking your work by plugging in values for the variables and simplifying the expression.
• Using a calculator to check your work.

Conclusion

In this article, we answered some frequently asked questions about subtracting polynomials. We covered topics such as identifying like terms, combining like terms, and simplifying the expression. We also discussed some common mistakes to avoid and some tips and tricks for subtracting polynomials. By following the steps outlined in this article, you can learn how to subtract polynomials and apply this knowledge to real-world problems.