Find The Value Of Each Expression When { E = -5 $}$, { F = 7 $}$, { G = 3 $}$.1. { E(f-g) - 5(7-3) $}$2. { (f+g)^2 $}$3. { 3e^2 - 4 $}$

In algebra, expressions are used to represent mathematical statements that involve variables and constants. Evaluating expressions with given values is an essential skill in mathematics, as it helps us to solve problems and make predictions. In this article, we will explore three algebraic expressions and find their values when $e = -5$, $f = 7$, and $g = 3$.

Expression 1: $e(f-g) - 5(7-3)$

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

1. Evaluate the expressions inside the parentheses: $f-g = 7-3 = 4$ and $7-3 = 4$.
2. Multiply $e$ by the result of $f-g$: $e(f-g) = -5(4) = -20$.
3. Multiply $5$ by the result of $7-3$: $5(7-3) = 5(4) = 20$.
4. Subtract the result of step 3 from the result of step 2: $e(f-g) - 5(7-3) = -20 - 20 = -40$.

Therefore, the value of the expression $e(f-g) - 5(7-3)$ is $-40$.

Expression 2: $(f+g)^2$

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

1. Add $f$ and $g$: $f+g = 7+3 = 10$.
2. Square the result of step 1: $(f+g)^2 = 10^2 = 100$.

Therefore, the value of the expression $(f+g)^2$ is $100$.

Expression 3: $3e^2 - 4$

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

1. Square $e$: $e^2 = (-5)^2 = 25$.
2. Multiply $3$ by the result of step 1: $3e^2 = 3(25) = 75$.
3. Subtract $4$ from the result of step 2: $3e^2 - 4 = 75 - 4 = 71$.

Therefore, the value of the expression $3e^2 - 4$ is $71$.

Conclusion

In this article, we evaluated three algebraic expressions with given values. We followed the order of operations (PEMDAS) to simplify each expression and find its value. The values of the expressions are $-40$, $100$, and $71$ respectively. These results demonstrate the importance of following the order of operations and simplifying expressions to find their values.

Tips and Tricks

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

Practice Problems

• Evaluate the expression $2x^2 + 5x - 3$ when $x = 2$.
• Simplify the expression $(x+2)^2 - 4$.
• Find the value of the expression $3(2x-1) + 2x^2$ when $x = 3$.

References

• "Algebra" by Michael Artin
• "Intermediate Algebra" by Charles P. McKeague
• "Algebra and Trigonometry" by James Stewart

In this article, we will answer some frequently asked questions about algebraic expressions. Whether you are a student or a teacher, these questions and answers will help you to better understand and work with algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical statement that involves variables and constants. It is a way to represent a mathematical relationship between variables and constants.

Q: What are the different parts of an algebraic expression?

A: An algebraic expression typically consists of the following parts:

• Variables: These are letters or symbols that represent unknown values. Examples of variables include x, y, and z.
• Constants: These are numbers that do not change value. Examples of constants include 2, 5, and 10.
• Operations: These are mathematical operations such as addition, subtraction, multiplication, and division.
• Parentheses: These are used to group expressions and avoid confusion.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need 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.

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

A: An expression is a mathematical statement that involves variables and constants, but it does not have an equal sign (=). An equation, on the other hand, is a mathematical statement that involves variables and constants, and it has an equal sign (=).

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and use the order of operations. Like terms are terms that have the same variable and exponent.

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that a single term can be distributed to multiple terms. For example, 2(x + 3) = 2x + 6.

Q: How do I use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, you need to multiply the single term by each of the multiple terms.

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

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when evaluating an algebraic expression. The acronym PEMDAS stands for:

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

Q: Why is it important to follow the order of operations?

A: Following the order of operations is important because it ensures that mathematical expressions are evaluated correctly and consistently.

Q: Can you provide some examples of algebraic expressions?

A: Yes, here are some examples of algebraic expressions:

• 2x + 3
• x^2 + 4x - 5
• 3(2x - 1) + 2x^2
• (x + 2)^2 - 4

Q: Can you provide some examples of algebraic equations?

A: Yes, here are some examples of algebraic equations:

• 2x + 3 = 5
• x^2 + 4x - 5 = 0
• 3(2x - 1) + 2x^2 = 10
• (x + 2)^2 - 4 = 9