We appreciate your visit to A greenhouse that specializes in growing geraniums is divided into sections The number of geranium pots in each section depends on the number of sprinklers. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Add the number of red geranium pots and the number of pink geranium pots: $x(7x-2) + (x+3)^2$.
- Expand the expression: $7x^2 - 2x + x^2 + 6x + 9$.
- Combine like terms: $7x^2 - 2x + x^2 + 6x + 9 = 8x^2 + 4x + 9$.
- The simplified expression is $\boxed{8 x^2+4 x+9}$.
### Explanation
1. Understanding the Problem
We are given the number of red geranium pots as $x(7x-2)$ and the number of pink geranium pots as $(x+3)^2$. We want to find the total number of red and pink geranium pots.
2. Setting up the Expression
To find the total number of pots, we add the number of red pots and the number of pink pots:$$x(7x-2) + (x+3)^2$$
3. Expanding the Terms
Now, we expand the expression:$$7x^2 - 2x + (x^2 + 6x + 9)$$
4. Combining Like Terms
Next, we combine like terms:$$7x^2 - 2x + x^2 + 6x + 9 = (7x^2 + x^2) + (-2x + 6x) + 9$$$$= 8x^2 + 4x + 9$$
5. Final Answer
Therefore, the simplified expression representing the total number of red and pink geranium pots in a section with $x$ sprinklers is $8x^2 + 4x + 9$.
### Examples
Understanding how to combine expressions like this is useful in many real-world scenarios. For example, if you're planning a garden, you might have different sections with varying numbers of plants based on sunlight or soil type. Being able to combine these expressions helps you calculate the total number of plants you need to buy or manage, making your gardening project more organized and efficient.
- Expand the expression: $7x^2 - 2x + x^2 + 6x + 9$.
- Combine like terms: $7x^2 - 2x + x^2 + 6x + 9 = 8x^2 + 4x + 9$.
- The simplified expression is $\boxed{8 x^2+4 x+9}$.
### Explanation
1. Understanding the Problem
We are given the number of red geranium pots as $x(7x-2)$ and the number of pink geranium pots as $(x+3)^2$. We want to find the total number of red and pink geranium pots.
2. Setting up the Expression
To find the total number of pots, we add the number of red pots and the number of pink pots:$$x(7x-2) + (x+3)^2$$
3. Expanding the Terms
Now, we expand the expression:$$7x^2 - 2x + (x^2 + 6x + 9)$$
4. Combining Like Terms
Next, we combine like terms:$$7x^2 - 2x + x^2 + 6x + 9 = (7x^2 + x^2) + (-2x + 6x) + 9$$$$= 8x^2 + 4x + 9$$
5. Final Answer
Therefore, the simplified expression representing the total number of red and pink geranium pots in a section with $x$ sprinklers is $8x^2 + 4x + 9$.
### Examples
Understanding how to combine expressions like this is useful in many real-world scenarios. For example, if you're planning a garden, you might have different sections with varying numbers of plants based on sunlight or soil type. Being able to combine these expressions helps you calculate the total number of plants you need to buy or manage, making your gardening project more organized and efficient.
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