Simplify The Expression:$\[ [(1+2) \times (-2)]^2 \\]

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Understanding the Expression

The given expression is [(1+2)×(−2)]2[(1+2) \times (-2)]^2. To simplify this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate the expressions inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  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.

Step 1: Evaluate the Expression Inside the Parentheses

The expression inside the parentheses is (1+2)(1+2). To evaluate this expression, we need to add 1 and 2.

(1+2)=3(1+2) = 3

Step 2: Multiply the Result by -2

Now that we have the result of the expression inside the parentheses, we can multiply it by -2.

3×(−2)=−63 \times (-2) = -6

Step 3: Raise the Result to the Power of 2

Finally, we need to raise the result to the power of 2.

(−6)2=36(-6)^2 = 36

Conclusion

Therefore, the simplified expression is 3636.

Understanding the Order of Operations

The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate the expressions inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  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.

Real-World Applications of the Order of Operations

The order of operations is used in many real-world applications, such as:

  • Science and Engineering: The order of operations is used to solve complex mathematical problems in science and engineering.
  • Finance: The order of operations is used to calculate financial formulas, such as interest rates and investment returns.
  • Computer Programming: The order of operations is used to write efficient and effective code.

Tips for Simplifying Expressions

Here are some tips for simplifying expressions:

  • Follow the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
  • Use parentheses: Use parentheses to group expressions and make it easier to simplify them.
  • Simplify inside the parentheses: Simplify expressions inside the parentheses before moving on to the next step.
  • Check your work: Check your work to make sure that you have simplified the expression correctly.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying expressions:

  • Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when simplifying expressions.
  • Not using parentheses: Use parentheses to group expressions and make it easier to simplify them.
  • Not simplifying inside the parentheses: Simplify expressions inside the parentheses before moving on to the next step.
  • Not checking your work: Check your work to make sure that you have simplified the expression correctly.

Conclusion

In conclusion, simplifying expressions is an important skill that is used in many real-world applications. By following the order of operations (PEMDAS) and using parentheses to group expressions, we can simplify complex expressions and make it easier to solve mathematical problems. Remember to check your work and avoid common mistakes to ensure that you have simplified the expression correctly.

Frequently Asked Questions

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 we have multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

  1. Parentheses: Evaluate the expressions inside the parentheses.
  2. Exponents: Evaluate any exponential expressions.
  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 important because it ensures that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may get incorrect results.

Q: What is the difference between parentheses and exponents?

A: Parentheses and exponents are both used to group expressions, but they serve different purposes. Parentheses are used to group expressions that need to be evaluated first, while exponents are used to indicate that an expression should be raised to a power.

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow the order of operations (PEMDAS). First, evaluate any expressions inside the parentheses. Next, evaluate any exponential expressions. Finally, evaluate any multiplication and division operations from left to right, and then evaluate any addition and subtraction operations from left to right.

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

  • Not following the order of operations
  • Not using parentheses to group expressions
  • Not simplifying expressions inside the parentheses
  • Not checking your work

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, follow these steps:

  1. Write down the original expression.
  2. Simplify the expression using the order of operations (PEMDAS).
  3. Check that your simplified expression is correct by plugging it back into the original expression.

Q: What are some real-world applications of the order of operations?

A: The order of operations is used in many real-world applications, such as:

  • Science and engineering
  • Finance
  • Computer programming

Q: How do I apply the order of operations in real-world situations?

A: To apply the order of operations in real-world situations, follow these steps:

  1. Identify the mathematical expression that needs to be evaluated.
  2. Follow the order of operations (PEMDAS) to simplify the expression.
  3. Use the simplified expression to solve the problem.

Q: What are some tips for simplifying expressions?

A: Some tips for simplifying expressions include:

  • Follow the order of operations (PEMDAS)
  • Use parentheses to group expressions
  • Simplify expressions inside the parentheses
  • Check your work

Q: How do I practice simplifying expressions?

A: To practice simplifying expressions, try the following:

  • Start with simple expressions and gradually move on to more complex ones.
  • Use online resources or math textbooks to practice simplifying expressions.
  • Work with a partner or tutor to practice simplifying expressions.

Conclusion

In conclusion, simplifying expressions is an important skill that is used in many real-world applications. By following the order of operations (PEMDAS) and using parentheses to group expressions, we can simplify complex expressions and make it easier to solve mathematical problems. Remember to check your work and avoid common mistakes to ensure that you have simplified the expression correctly.