Consider This Expression:${ M^2 - 7 \mid + N^2 }$When { M = -2 $}$ And { N = 5 $}$, The Value Of The Expression Is { \square$}$. Type The Correct Answer In The Box. Use Numerals Instead Of Words.

Introduction

Algebraic expressions are a fundamental concept in mathematics, and understanding how to evaluate them is crucial for solving various mathematical problems. In this article, we will focus on evaluating the expression $m^2 - 7 \mid + n^2$ when $m = -2$ and $n = 5$. We will break down the expression into smaller parts, evaluate each part, and then combine the results to obtain the final answer.

Understanding the Expression

The given expression is $m^2 - 7 \mid + n^2$. This expression consists of three main parts:

1. $m^2$: This is the square of the variable $m$.
2. $-7 \mid$: This is a constant term, where $-7$ is subtracted from the result of the first part.
3. $n^2$: This is the square of the variable $n$.

Evaluating the Expression

To evaluate the expression, we need to substitute the values of $m$ and $n$ into the expression. We are given that $m = -2$ and $n = 5$. Substituting these values into the expression, we get:

$(-2)^2 - 7 \mid + (5)^2$

Step 1: Evaluate the Squares

The first step is to evaluate the squares of $m$ and $n$. We have:

$(-2)^2 = 4$

$(5)^2 = 25$

Step 2: Substitute the Values

Now that we have evaluated the squares, we can substitute the values into the expression:

$4 - 7 \mid + 25$

Step 3: Evaluate the Expression

The next step is to evaluate the expression. We have:

$4 - 7 \mid + 25$

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expression inside the absolute value sign: $-7 \mid = -7$
2. Subtract $-7$ from $4$: $4 - (-7) = 4 + 7 = 11$
3. Add $25$ to the result: $11 + 25 = 36$

Conclusion

In this article, we evaluated the expression $m^2 - 7 \mid + n^2$ when $m = -2$ and $n = 5$. We broke down the expression into smaller parts, evaluated each part, and then combined the results to obtain the final answer. The final answer is $\boxed{36}$.

Tips and Tricks

• When evaluating algebraic expressions, always follow the order of operations (PEMDAS).
• Make sure to substitute the values of variables into the expression correctly.
• Break down complex expressions into smaller parts to make them easier to evaluate.

Common Mistakes

• Failing to follow the order of operations (PEMDAS).
• Not substituting the values of variables into the expression correctly.
• Not breaking down complex expressions into smaller parts.

Real-World Applications

Algebraic expressions are used in various real-world applications, such as:

• Physics: Algebraic expressions are used to describe the motion of objects and the behavior of physical systems.
• Engineering: Algebraic expressions are used to design and optimize systems, such as electrical circuits and mechanical systems.
• Economics: Algebraic expressions are used to model economic systems and make predictions about economic trends.

Conclusion

$$$$$$$$

Introduction

In our previous article, we evaluated the expression $m^2 - 7 \mid + n^2$ when $m = -2$ and $n = 5$. We broke down the expression into smaller parts, evaluated each part, and then combined the results to obtain the final answer. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

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 evaluating an expression. The acronym PEMDAS stands for:

• Parentheses: Evaluate expressions inside parentheses first.
• Exponents: Evaluate any exponential expressions next (e.g., $2^3$).
• Multiplication and Division: Evaluate any multiplication and division operations from left to right.
• Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate an expression with absolute value?

A: When evaluating an expression with absolute value, you need to follow these steps:

1. Evaluate the expression inside the absolute value sign.
2. If the result is positive, the absolute value is the same as the result.
3. If the result is negative, the absolute value is the positive version of the result.

For example, if we have the expression $|-3|$, we would evaluate the expression inside the absolute value sign, which is $-3$. Since $-3$ is negative, the absolute value is $3$.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change. For example, $x$ is a variable. A constant is a value that does not change. For example, $5$ is a constant.

Q: How do I evaluate an expression with multiple variables?

A: When evaluating an expression with multiple variables, you need to follow these steps:

1. Substitute the values of the variables into the expression.
2. Evaluate the expression using the order of operations (PEMDAS).
3. Simplify the expression to obtain the final answer.

For example, if we have the expression $x^2 + 3y - 2$, and we are given that $x = 2$ and $y = 3$, we would substitute the values of $x$ and $y$ into the expression, which would give us $2^2 + 3(3) - 2$. We would then evaluate the expression using the order of operations (PEMDAS), which would give us $4 + 9 - 2 = 11$.

Q: What is the difference between an expression and an equation?

A: An expression is a group of numbers, variables, and mathematical operations that are combined using various rules. For example, $x^2 + 3y - 2$ is an expression. An equation is a statement that says two expressions are equal. For example, $x^2 + 3y - 2 = 5$ is an equation.

Q: How do I solve an equation with multiple variables?

A: When solving an equation with multiple variables, you need to follow these steps:

1. Substitute the values of the variables into the equation.
2. Evaluate the equation using the order of operations (PEMDAS).
3. Simplify the equation to obtain the final answer.

For example, if we have the equation $x^2 + 3y - 2 = 5$, and we are given that $x = 2$ and $y = 3$, we would substitute the values of $x$ and $y$ into the equation, which would give us $2^2 + 3(3) - 2 = 5$. We would then evaluate the equation using the order of operations (PEMDAS), which would give us $4 + 9 - 2 = 11$. Since $11$ is not equal to $5$, we would need to try different values of $x$ and $y$ to find the solution.

Conclusion

In conclusion, evaluating algebraic expressions is a crucial skill in mathematics. By following the order of operations (PEMDAS) and breaking down complex expressions into smaller parts, we can evaluate expressions accurately and efficiently. We hope that this Q&A guide has helped you to better understand how to evaluate algebraic expressions and solve equations with multiple variables.