Evaluate A 2 − 3 B A^2 - 3b A 2 − 3 B When A = 2 A = 2 A = 2 And B = − 3 B = -3 B = − 3 .A. 6 B. 11 C. 15 D. 9 E. -5 F. 13

Mar 9, 2025 by ADMIN 128 views

Evaluate $a^2 - 3b$ when $a = 2$ and $b = -3$

Understanding the Problem

To evaluate the expression $a^2 - 3b$ when $a = 2$ and $b = -3$ , we need to substitute the given values of $a$ and $b$ into the expression and then simplify it. This involves basic algebraic operations such as squaring, multiplication, and subtraction.

Substituting Values into the Expression

We are given that $a = 2$ and $b = -3$ . To substitute these values into the expression $a^2 - 3b$ , we replace $a$ with $2$ and $b$ with $-3$ . This gives us:

2^2 - 3(-3)

Simplifying the Expression

Now that we have substituted the values, we can simplify the expression by following the order of operations (PEMDAS):

Squaring the value of $a$ : $2^2 = 4$
Multiplying $3$ by the value of $b$ : $3(-3) = -9$
Subtracting the result of step 2 from the result of step 1: $4 - (-9) = 4 + 9 = 13$

Evaluating the Expression

Therefore, when $a = 2$ and $b = -3$ , the value of the expression $a^2 - 3b$ is $13$ .

Conclusion

In this problem, we evaluated the expression $a^2 - 3b$ when $a = 2$ and $b = -3$ . We substituted the given values into the expression, simplified it by following the order of operations, and arrived at the final answer of $13$ .

Common Mistakes to Avoid

When evaluating expressions with variables, it's essential to follow the order of operations (PEMDAS) and substitute values correctly. Some common mistakes to avoid include:

Not following the order of operations: Failing to evaluate expressions in the correct order can lead to incorrect results.
Incorrect substitution of values: Substituting values incorrectly can result in incorrect expressions.
Not simplifying expressions: Failing to simplify expressions can make it difficult to arrive at the final answer.

Real-World Applications

Evaluating expressions with variables is a fundamental concept in mathematics and has numerous real-world applications. Some examples include:

Science and engineering: Evaluating expressions with variables is crucial in scientific and engineering applications, such as calculating distances, velocities, and forces.
Finance: Evaluating expressions with variables is essential in finance, such as calculating interest rates, investment returns, and stock prices.
Computer programming: Evaluating expressions with variables is a fundamental concept in computer programming, such as writing algorithms and creating mathematical models.

Final Answer

The final answer is $\boxed{13}$ .

Introduction

Evaluating expressions with variables is a fundamental concept in mathematics that has numerous real-world applications. In this article, we will provide a Q&A guide to help you understand and evaluate expressions with variables.

Q: What is an expression with variables?

A: An expression with variables is a mathematical statement that contains variables, constants, and mathematical operations. Variables are letters or symbols that represent unknown values, while constants are numbers that do not change.

Q: How do I evaluate an expression with variables?

A: To evaluate an expression with variables, you need to substitute the given values of the variables into the expression and then simplify it by following the order of operations (PEMDAS).

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 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 substitute values into an expression with variables?

A: To substitute values into an expression with variables, you need to replace the variables with the given values. For example, if the expression is 2x + 3 and the value of x is 4, you would substitute 4 for x to get 2(4) + 3.

Q: What are some common mistakes to avoid when evaluating expressions with variables?

A: Some common mistakes to avoid when evaluating expressions with variables include:

Not following the order of operations: Failing to evaluate expressions in the correct order can lead to incorrect results.
Incorrect substitution of values: Substituting values incorrectly can result in incorrect expressions.
Not simplifying expressions: Failing to simplify expressions can make it difficult to arrive at the final answer.

Q: How do I simplify an expression with variables?

A: To simplify an expression with variables, you need to combine like terms and eliminate any unnecessary operations. For example, if the expression is 2x + 3 + 2x, you can combine the like terms to get 4x + 3.

Q: What are some real-world applications of evaluating expressions with variables?

A: Evaluating expressions with variables has numerous real-world applications, including:

Science and engineering: Evaluating expressions with variables is crucial in scientific and engineering applications, such as calculating distances, velocities, and forces.
Finance: Evaluating expressions with variables is essential in finance, such as calculating interest rates, investment returns, and stock prices.
Computer programming: Evaluating expressions with variables is a fundamental concept in computer programming, such as writing algorithms and creating mathematical models.

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

A: To evaluate an expression with multiple variables, you need to substitute the given values of all the variables into the expression and then simplify it by following the order of operations (PEMDAS).

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

A: A variable is a letter or symbol that represents an unknown value, while a constant is a number that does not change.

Q: How do I determine the value of a variable?

A: To determine the value of a variable, you need to substitute the given values of the variables into the expression and then simplify it by following the order of operations (PEMDAS).

Q: What are some common types of expressions with variables?

A: Some common types of expressions with variables include:

Linear expressions: Expressions that contain a single variable and a constant, such as 2x + 3.
Quadratic expressions: Expressions that contain a single variable squared and a constant, such as x^2 + 3x + 2.
Polynomial expressions: Expressions that contain multiple variables and constants, such as 2x^2 + 3x + 2.

Q: How do I evaluate a polynomial expression with variables?

A: To evaluate a polynomial expression with variables, you need to substitute the given values of the variables into the expression and then simplify it by following the order of operations (PEMDAS).

Q: What are some common mistakes to avoid when evaluating polynomial expressions with variables?

A: Some common mistakes to avoid when evaluating polynomial expressions with variables include:

Not following the order of operations: Failing to evaluate expressions in the correct order can lead to incorrect results.
Incorrect substitution of values: Substituting values incorrectly can result in incorrect expressions.
Not simplifying expressions: Failing to simplify expressions can make it difficult to arrive at the final answer.

Q: How do I simplify a polynomial expression with variables?

A: To simplify a polynomial expression with variables, you need to combine like terms and eliminate any unnecessary operations.

Q: What are some real-world applications of evaluating polynomial expressions with variables?

A: Evaluating polynomial expressions with variables has numerous real-world applications, including:

Science and engineering: Evaluating polynomial expressions with variables is crucial in scientific and engineering applications, such as calculating distances, velocities, and forces.
Finance: Evaluating polynomial expressions with variables is essential in finance, such as calculating interest rates, investment returns, and stock prices.
Computer programming: Evaluating polynomial expressions with variables is a fundamental concept in computer programming, such as writing algorithms and creating mathematical models.

Conclusion

Evaluating expressions with variables is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations (PEMDAS) and substituting values correctly, you can simplify expressions and arrive at the final answer. Remember to avoid common mistakes such as not following the order of operations, incorrect substitution of values, and not simplifying expressions.