Evaluate The Expression:$(3 \times 4)^2 =$

by ADMIN 45 views

Introduction

In mathematics, expressions are a fundamental concept that helps us represent and solve problems. Evaluating an expression involves substituting values into the expression and simplifying it to obtain a final result. In this article, we will evaluate the expression (3×4)2(3 \times 4)^2 and explore the steps involved in simplifying it.

Understanding the Expression

The given expression is (3×4)2(3 \times 4)^2. To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: Evaluate any exponents (such as squaring or cubing).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

Let's start by evaluating the expression inside the parentheses:

(3×4)(3 \times 4)

To evaluate this expression, we need to multiply 3 and 4:

(3×4)=12(3 \times 4) = 12

Now that we have evaluated the expression inside the parentheses, we can substitute the result into the original expression:

(3×4)2=122(3 \times 4)^2 = 12^2

Simplifying the Expression

The next step is to evaluate the exponent (squaring) of 12:

122=14412^2 = 144

Therefore, the final result of the expression (3×4)2(3 \times 4)^2 is 144.

Conclusion

Evaluating an expression involves following the order of operations and simplifying it to obtain a final result. In this article, we evaluated the expression (3×4)2(3 \times 4)^2 and explored the steps involved in simplifying it. By following the order of operations and simplifying the expression, we obtained a final result of 144.

Real-World Applications

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. For example, in finance, evaluating expressions is used to calculate interest rates, investment returns, and other financial metrics. In science, evaluating expressions is used to model and analyze complex systems, such as population growth and chemical reactions.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions:

  • Follow the order of operations: Always follow the order of operations (PEMDAS) when evaluating an expression.
  • Simplify the expression: Simplify the expression as much as possible before evaluating it.
  • Use parentheses: Use parentheses to group expressions and make them easier to evaluate.
  • Check your work: Always check your work to ensure that you have evaluated the expression correctly.

Common Mistakes

Here are some common mistakes to avoid when evaluating expressions:

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
  • Not simplifying the expression: Failing to simplify the expression can make it more difficult to evaluate.
  • Not using parentheses: Failing to use parentheses can make the expression more difficult to evaluate.
  • Not checking your work: Failing to check your work can lead to incorrect results.

Final Thoughts

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations and simplifying the expression, you can obtain a final result that is accurate and reliable. Remember to follow the tips and tricks outlined in this article, and avoid the common mistakes that can lead to incorrect results. With practice and patience, you will become proficient in evaluating expressions and solving complex mathematical problems.

Introduction

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. In our previous article, we explored the steps involved in evaluating the expression (3×4)2(3 \times 4)^2. In this article, we will answer some frequently asked questions about evaluating expressions.

Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:

  1. Parentheses: Evaluate the expression inside the parentheses.
  2. Exponents: Evaluate any exponents (such as squaring or cubing).
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

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

A: Following the order of operations is crucial when evaluating expressions because it ensures that we perform the operations in the correct order. If we don't follow the order of operations, we may get incorrect results.

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

A: An expression is a mathematical statement that contains variables, constants, and operators. An equation is a mathematical statement that contains an expression on one side and an equal sign (=) on the other side.

Q: How do I simplify an expression?

A: To simplify an expression, we need to combine like terms and eliminate any unnecessary operations. We can simplify an expression by:

  • Combining like terms: Combine terms that have the same variable and coefficient.
  • Eliminating unnecessary operations: Remove any operations that are not necessary to evaluate the expression.

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

A: A variable is a symbol that represents a value that can change. A constant is a value that does not change.

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, we need to follow the order of operations. We need to evaluate any exponents (such as squaring or cubing) before performing any multiplication or division operations.

Q: What is the difference between a positive exponent and a negative exponent?

A: A positive exponent indicates that we need to multiply the base by itself as many times as the exponent. A negative exponent indicates that we need to divide 1 by the base as many times as the exponent.

Q: How do I evaluate an expression with parentheses?

A: To evaluate an expression with parentheses, we need to follow the order of operations. We need to evaluate any expressions inside the parentheses before performing any other operations.

Q: What is the difference between an expression and a formula?

A: An expression is a mathematical statement that contains variables, constants, and operators. A formula is a mathematical statement that contains variables, constants, and operators, and is used to solve a specific problem.

Q: How do I check my work when evaluating an expression?

A: To check your work when evaluating an expression, you can:

  • Plug in values for the variables and evaluate the expression.
  • Use a calculator to evaluate the expression.
  • Check your work by re-evaluating the expression.

Conclusion

Evaluating expressions is a fundamental concept in mathematics that has numerous real-world applications. By following the order of operations and simplifying the expression, you can obtain a final result that is accurate and reliable. Remember to follow the tips and tricks outlined in this article, and avoid the common mistakes that can lead to incorrect results. With practice and patience, you will become proficient in evaluating expressions and solving complex mathematical problems.

Final Thoughts

Evaluating expressions is a crucial skill that is used in many areas of mathematics and science. By mastering the skills outlined in this article, you will be able to evaluate expressions with confidence and accuracy. Remember to always follow the order of operations and simplify the expression to obtain a final result that is accurate and reliable.