Evaluate A 2 + A A^2 + A A 2 + A If A = − 5 A = -5 A = − 5 .

$$$$

Introduction

In mathematics, evaluating expressions is a crucial skill that helps us solve problems and understand the behavior of functions. In this article, we will evaluate the expression $a^2 + a$ when $a = -5$. This involves substituting the value of $a$ into the expression and simplifying it to obtain the final result.

Understanding the Expression

The expression $a^2 + a$ is a quadratic expression, which is a polynomial of degree two. It consists of two terms: $a^2$ and $a$. The first term is the square of $a$, while the second term is $a$ itself. When we substitute a value for $a$, we need to follow the order of operations (PEMDAS) to simplify the expression.

Substituting $a = -5$

To evaluate the expression $a^2 + a$ when $a = -5$, we need to substitute $-5$ for $a$ in the expression. This gives us:

$$(-5)^2 + (-5)$$

Simplifying the Expression

Now, we need to simplify the expression by following the order of operations. First, we need to evaluate the exponentiation:

$$(-5)^2 = 25$$

Next, we need to multiply $-5$ by $-5$:

$$(-5) \times (-5) = 25$$

Combining the Terms

Now that we have evaluated the exponentiation and multiplication, we can combine the terms:

$$25 + (-5)$$

Final Result

To simplify the expression further, we need to combine the terms. Since $25$ is a positive number and $-5$ is a negative number, we can add them together:

$$25 + (-5) = 20$$

Therefore, the final result is $20$.

Conclusion

In this article, we evaluated the expression $a^2 + a$ when $a = -5$. We substituted the value of $a$ into the expression, followed the order of operations, and simplified the expression to obtain the final result. This demonstrates the importance of following the order of operations and simplifying expressions to obtain the correct result.

Tips and Tricks

• When evaluating expressions, always follow the order of operations (PEMDAS).
• Simplify expressions by combining like terms.
• Use parentheses to group terms and avoid confusion.
• Check your work by plugging in different values for the variable.

Real-World Applications

Evaluating expressions is a crucial skill in many real-world applications, including:

• Science: Evaluating expressions is essential in scientific calculations, such as calculating the trajectory of a projectile or the energy of a system.
• Engineering: Evaluating expressions is critical in engineering calculations, such as designing bridges or buildings.
• Finance: Evaluating expressions is essential in financial calculations, such as calculating interest rates or investment returns.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not simplifying expressions by combining like terms.
• Using incorrect values for the variable.
• Not checking work by plugging in different values for the variable.

Final Thoughts

Evaluating expressions is a fundamental skill in mathematics that helps us solve problems and understand the behavior of functions. By following the order of operations, simplifying expressions, and checking our work, we can ensure that we obtain the correct result. This skill is essential in many real-world applications, and it is crucial to practice and master it to become proficient in mathematics.

$$$$

Introduction

In our previous article, we evaluated the expression $a^2 + a$ when $a = -5$. We substituted the value of $a$ into the expression, followed the order of operations, and simplified the expression to obtain the final result. In this article, we will answer some frequently asked questions about evaluating expressions, including the expression $a^2 + a$.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., $2^3$).
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: How do I simplify an expression?

A: To simplify an expression, follow these steps:

1. Evaluate any exponential expressions.
2. Evaluate any multiplication and division operations from left to right.
3. Evaluate any addition and subtraction operations from left to right.
4. Combine like terms (e.g., $2x + 3x = 5x$).

Q: What is the difference between $a^2$ and $a$?

A: $a^2$ is the square of $a$, which means we multiply $a$ by itself: $a^2 = a \times a$. On the other hand, $a$ is just the variable itself.

Q: How do I evaluate an expression with a negative number?

A: When evaluating an expression with a negative number, remember to follow the order of operations (PEMDAS). For example, if we have the expression $(-5)^2 + (-5)$, we would first evaluate the exponentiation: $(-5)^2 = 25$. Then, we would multiply $-5$ by $-5$: $(-5) \times (-5) = 25$. Finally, we would add the two terms: $25 + (-5) = 20$.

Q: Can I use a calculator to evaluate an expression?

A: Yes, you can use a calculator to evaluate an expression. However, it's always a good idea to check your work by plugging in different values for the variable.

Q: What is the final result of $a^2 + a$ when $a = -5$?

A: The final result of $a^2 + a$ when $a = -5$ is $20$.

Conclusion

Evaluating expressions is a fundamental skill in mathematics that helps us solve problems and understand the behavior of functions. By following the order of operations, simplifying expressions, and checking our work, we can ensure that we obtain the correct result. We hope this Q&A article has helped you understand how to evaluate expressions, including the expression $a^2 + a$.

Tips and Tricks

• Always follow the order of operations (PEMDAS).
• Simplify expressions by combining like terms.
• Use parentheses to group terms and avoid confusion.
• Check your work by plugging in different values for the variable.

Real-World Applications

Evaluating expressions is a crucial skill in many real-world applications, including:

• Science: Evaluating expressions is essential in scientific calculations, such as calculating the trajectory of a projectile or the energy of a system.
• Engineering: Evaluating expressions is critical in engineering calculations, such as designing bridges or buildings.
• Finance: Evaluating expressions is essential in financial calculations, such as calculating interest rates or investment returns.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not simplifying expressions by combining like terms.
• Using incorrect values for the variable.
• Not checking work by plugging in different values for the variable.

Final Thoughts

Evaluating expressions is a fundamental skill in mathematics that helps us solve problems and understand the behavior of functions. By following the order of operations, simplifying expressions, and checking our work, we can ensure that we obtain the correct result. This skill is essential in many real-world applications, and it is crucial to practice and master it to become proficient in mathematics.