The Volume Of A Small Packing Box Is $3x^2 + 3x$ In³ Smaller Than A Large Packing Box With A Volume Of $5x^2 - 2x + 10$ In³. Find A Single Expression That Represents The Size Of A Small Packing Box.A. 2 X 2 − 2 X + 10 2x^2 - 2x + 10 2 X 2 − 2 X + 10 B.

Introduction

When it comes to packing boxes, understanding their volumes is crucial for efficient storage and transportation. In this article, we will delve into the world of mathematics to find a single expression that represents the size of a small packing box. Given that the volume of a small packing box is $3x^2 + 3x$ in³ smaller than a large packing box with a volume of $5x^2 - 2x + 10$ in³, we will use algebraic techniques to derive the volume of the small packing box.

Understanding the Problem

To find the volume of the small packing box, we need to subtract the volume of the small box from the volume of the large box. This can be represented mathematically as:

Volume of large box - Volume of small box = Volume of small box

Substituting the given volumes, we get:

$$5x^2 - 2x + 10 - (3x^2 + 3x) = 3x^2 + 3x$$

Simplifying the Expression

To simplify the expression, we need to combine like terms. We can start by distributing the negative sign to the terms inside the parentheses:

$$5x^2 - 2x + 10 - 3x^2 - 3x = 3x^2 + 3x$$

Next, we can combine the like terms:

$$5x^2 - 3x^2 - 2x - 3x + 10 = 3x^2 + 3x$$

Simplifying further, we get:

$$2x^2 - 5x + 10 = 3x^2 + 3x$$

Finding the Volume of the Small Packing Box

Now that we have simplified the expression, we can find the volume of the small packing box by subtracting the volume of the small box from the volume of the large box:

$$5x^2 - 2x + 10 - (2x^2 - 5x + 10) = 3x^2 + 3x$$

Distributing the negative sign to the terms inside the parentheses, we get:

$$5x^2 - 2x + 10 - 2x^2 + 5x - 10 = 3x^2 + 3x$$

Combining like terms, we get:

$$3x^2 + 3x = 3x^2 + 3x$$

This confirms that the volume of the small packing box is indeed $3x^2 + 3x$ in³.

Conclusion

In this article, we used algebraic techniques to find a single expression that represents the size of a small packing box. By subtracting the volume of the small box from the volume of the large box, we were able to derive the volume of the small packing box. The final expression is $3x^2 + 3x$ in³, which represents the size of the small packing box.

Final Answer

The final answer is: $\boxed{3x^2 + 3x}$

Introduction

In our previous article, we explored the concept of finding a single expression that represents the size of a small packing box. We used algebraic techniques to derive the volume of the small packing box, which is $3x^2 + 3x$ in³. In this article, we will answer some frequently asked questions related to this topic.

Q&A

Q: What is the volume of the large packing box?

A: The volume of the large packing box is given as $5x^2 - 2x + 10$ in³.

Q: How do we find the volume of the small packing box?

A: To find the volume of the small packing box, we need to subtract the volume of the small box from the volume of the large box. This can be represented mathematically as:

Volume of large box - Volume of small box = Volume of small box

Q: What is the difference between the volume of the large and small packing boxes?

A: The difference between the volume of the large and small packing boxes is $3x^2 + 3x$ in³.

Q: Can we simplify the expression for the volume of the small packing box?

A: Yes, we can simplify the expression for the volume of the small packing box by combining like terms. The simplified expression is $3x^2 + 3x$ in³.

Q: How do we distribute the negative sign to the terms inside the parentheses?

A: To distribute the negative sign to the terms inside the parentheses, we need to multiply each term by -1. For example, if we have the expression $- (3x^2 + 3x)$, we can distribute the negative sign as follows:

$$-3x^2 - 3x$$

Q: What is the final expression for the volume of the small packing box?

A: The final expression for the volume of the small packing box is $3x^2 + 3x$ in³.

Conclusion

In this article, we answered some frequently asked questions related to finding a single expression that represents the size of a small packing box. We used algebraic techniques to derive the volume of the small packing box and simplified the expression to $3x^2 + 3x$ in³. We hope that this article has provided a clear understanding of the concept and has helped to clarify any doubts.

Final Answer

The final answer is: $\boxed{3x^2 + 3x}$