Iliana Cubed The Number Of Flowering Plants In Her Garden, Then Added 2 Vegetable Plants. Let $p$ Represent The Original Number Of Plants In Her Garden. Which Shows An Expression To Represent The Total Number Of Plants In Her Garden And The

Introduction

In this article, we will delve into the world of mathematics and explore how to represent the total number of plants in Iliana's garden. We will use algebraic expressions to model the situation and provide a clear understanding of the mathematical concepts involved.

The Original Number of Plants

Let's assume that the original number of plants in Iliana's garden is represented by the variable $p$. This variable will be used to represent the total number of flowering plants in the garden.

Cubing the Number of Flowering Plants

Iliana cubed the number of flowering plants in her garden. This means that she raised the number of flowering plants to the power of 3. In mathematical terms, this can be represented as $p^3$.

Adding Vegetable Plants

After cubing the number of flowering plants, Iliana added 2 vegetable plants to the garden. This can be represented as $2$.

Representing the Total Number of Plants

To find the total number of plants in Iliana's garden, we need to add the cubed number of flowering plants and the 2 vegetable plants. This can be represented as:

$$p^3 + 2$$

This expression represents the total number of plants in Iliana's garden.

Discussion

The expression $p^3 + 2$ represents the total number of plants in Iliana's garden. This expression is an example of an algebraic expression, which is a mathematical expression that contains variables and constants.

In this expression, the variable $p$ represents the original number of plants in the garden, and the constant $2$ represents the number of vegetable plants added to the garden. The exponent $3$ represents the fact that the number of flowering plants was cubed.

Conclusion

In conclusion, the expression $p^3 + 2$ represents the total number of plants in Iliana's garden. This expression is an example of an algebraic expression, which is a mathematical expression that contains variables and constants.

Real-World Applications

Algebraic expressions like $p^3 + 2$ have many real-world applications. For example, they can be used to model population growth, financial transactions, and scientific experiments.

Tips and Tricks

When working with algebraic expressions, it's essential to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

By following the order of operations, you can ensure that your algebraic expressions are evaluated correctly.

Common Mistakes

When working with algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not following the order of operations (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

By avoiding these common mistakes, you can ensure that your algebraic expressions are evaluated correctly.

Conclusion

In conclusion, the expression $p^3 + 2$ represents the total number of plants in Iliana's garden. This expression is an example of an algebraic expression, which is a mathematical expression that contains variables and constants.

Introduction

In our previous article, we explored how to represent the total number of plants in Iliana's garden using algebraic expressions. We introduced the variable $p$ to represent the original number of plants in the garden and used the expression $p^3 + 2$ to represent the total number of plants.

Q&A

Q: What is the original number of plants in Iliana's garden? A: The original number of plants in Iliana's garden is represented by the variable $p$.

Q: What does the expression $p^3$ represent? A: The expression $p^3$ represents the number of flowering plants in Iliana's garden after cubing the original number of plants.

Q: What does the expression $2$ represent? A: The expression $2$ represents the number of vegetable plants added to Iliana's garden.

Q: What is the total number of plants in Iliana's garden? A: The total number of plants in Iliana's garden is represented by the expression $p^3 + 2$.

Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that dictates the order in which mathematical operations should be performed. The order is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Why is it essential to follow the order of operations (PEMDAS)? A: Following the order of operations (PEMDAS) ensures that mathematical expressions are evaluated correctly and consistently.

Q: What are some common mistakes to avoid when working with algebraic expressions? A: Some common mistakes to avoid when working with algebraic expressions include:

• Not following the order of operations (PEMDAS)
• Not evaluating expressions inside parentheses first
• Not evaluating exponential expressions next
• Not evaluating multiplication and division operations from left to right
• Not evaluating addition and subtraction operations from left to right

Q: How can I apply algebraic expressions to real-world situations? A: Algebraic expressions can be applied to a wide range of real-world situations, including:

• Modeling population growth
• Financial transactions
• Scientific experiments
• Engineering design

Conclusion

In conclusion, the expression $p^3 + 2$ represents the total number of plants in Iliana's garden. By understanding algebraic expressions and following the order of operations (PEMDAS), you can model real-world situations and solve mathematical problems with ease.

Additional Resources

For further learning and practice, we recommend the following resources:

• Khan Academy: Algebra
• Mathway: Algebra Solver
• Wolfram Alpha: Algebra Calculator

Practice Problems

Try your hand at solving the following practice problems:

1. If the original number of plants in Iliana's garden is 5, what is the total number of plants in the garden?
2. If the number of flowering plants in Iliana's garden is cubed, and then 2 vegetable plants are added, what is the total number of plants in the garden?
3. If the original number of plants in Iliana's garden is represented by the variable $x$, what is the total number of plants in the garden?

Answer Key

1. $5^3 + 2 = 133$
2. $p^3 + 2$
3. $x^3 + 2$