Simplify The Expression: ( 2 − 6 ) ⋅ ( − 5 + 12 (2-6) \cdot (-5+12 ( 2 − 6 ) ⋅ ( − 5 + 12 ]

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing unnecessary operations, and rearranging the expression to make it easier to work with. In this article, we will simplify the expression $(2-6) \cdot (-5+12)$ using basic algebraic operations.

Understanding the Expression

The given expression is a product of two binomials: $(2-6)$ and $(-5+12)$. To simplify this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the expressions inside the parentheses.
2. Multiply the results.

Step 1: Evaluate the Expressions Inside the Parentheses

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

• $(2-6) = -4$
• $(-5+12) = 7$

Step 2: Multiply the Results

Now that we have the values of the expressions inside the parentheses, we can multiply them:

$(-4) \cdot (7) = -28$

Simplifying the Expression

Therefore, the simplified expression is $-28$.

Why Simplifying Expressions is Important

Simplifying expressions is an essential skill in mathematics because it helps us:

• Reduce errors: Simplifying expressions reduces the likelihood of errors, as we are working with a simpler expression.
• Save time: Simplifying expressions saves time, as we can work with a simpler expression and avoid unnecessary calculations.
• Improve understanding: Simplifying expressions helps us understand the underlying structure of the expression and how it relates to other mathematical concepts.

Real-World Applications of Simplifying Expressions

Simplifying expressions has numerous real-world applications, including:

• Science and engineering: Simplifying expressions is crucial in science and engineering, where complex mathematical models are used to describe real-world phenomena.
• Finance: Simplifying expressions is essential in finance, where complex financial models are used to analyze and predict market trends.
• Computer programming: Simplifying expressions is a fundamental concept in computer programming, where complex algorithms are used to solve problems.

Conclusion

In conclusion, simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently. By following the order of operations and simplifying expressions, we can reduce errors, save time, and improve our understanding of mathematical concepts. Whether you are a student, a professional, or simply someone who enjoys mathematics, simplifying expressions is an essential skill that can benefit you in many ways.

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 working with mathematical expressions. The order of operations is:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

Q: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow the order of operations and simplify each operation one at a time. For example, if you have the expression $(2+3) \cdot (4-5)$, first simplify the expressions inside the parentheses, then multiply the results.

Q: Why is simplifying expressions important in science and engineering?

A: Simplifying expressions is crucial in science and engineering because complex mathematical models are used to describe real-world phenomena. By simplifying expressions, scientists and engineers can reduce errors, save time, and improve their understanding of complex systems.

Q: Can I use a calculator to simplify expressions?

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 working with mathematical expressions. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
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: How do I simplify expressions with multiple operations?

A: To simplify expressions with multiple operations, follow the order of operations and simplify each operation one at a time. For example, if you have the expression $(2+3) \cdot (4-5)$, first simplify the expressions inside the parentheses, then multiply the results.

Q: What is the difference between simplifying expressions and evaluating expressions?

A: Simplifying expressions involves combining like terms, removing unnecessary operations, and rearranging the expression to make it easier to work with. Evaluating expressions, on the other hand, involves substituting values into the expression and calculating the result.

Q: Can I use a calculator to simplify expressions?

A: Yes, you can use a calculator to simplify expressions. However, it's essential to understand the underlying mathematical concepts and be able to simplify expressions manually, as this will help you develop a deeper understanding of mathematics and improve your problem-solving skills.

Q: How do I simplify expressions with negative numbers?

A: To simplify expressions with negative numbers, follow the same rules as for positive numbers. For example, if you have the expression $(-2+3) \cdot (-4-5)$, first simplify the expressions inside the parentheses, then multiply the results.

Q: Can I simplify expressions with variables?

A: Yes, you can simplify expressions with variables. To do this, follow the same rules as for numerical expressions, and use the properties of variables to simplify the expression. For example, if you have the expression $2x + 3x$, you can combine like terms to get $5x$.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, follow the same rules as for numerical expressions, and use the properties of fractions to simplify the expression. For example, if you have the expression $\frac{1}{2} + \frac{1}{3}$, you can find a common denominator and add the fractions.

Q: Can I simplify expressions with exponents?

A: Yes, you can simplify expressions with exponents. To do this, follow the same rules as for numerical expressions, and use the properties of exponents to simplify the expression. For example, if you have the expression $2^3 \cdot 2^2$, you can combine the exponents to get $2^5$.

Q: How do I simplify expressions with absolute values?

A: To simplify expressions with absolute values, follow the same rules as for numerical expressions, and use the properties of absolute values to simplify the expression. For example, if you have the expression $|2-3|$, you can evaluate the expression inside the absolute value to get $|-1|$.

Conclusion

In conclusion, simplifying expressions is a crucial skill in mathematics that helps us solve problems efficiently. By following the order of operations and simplifying expressions, we can reduce errors, save time, and improve our understanding of mathematical concepts. Whether you are a student, a professional, or simply someone who enjoys mathematics, simplifying expressions is an essential skill that can benefit you in many ways.

Additional Resources

• Math textbooks: Check out your local library or online resources for math textbooks that provide detailed explanations and examples of simplifying expressions.
• Online tutorials: Websites like Khan Academy, Mathway, and Wolfram Alpha offer interactive tutorials and examples of simplifying expressions.
• Practice problems: Try solving practice problems on your own or with a study group to reinforce your understanding of simplifying expressions.

Final Tips

• Practice regularly: Simplifying expressions is a skill that requires practice to develop. Make sure to practice regularly to improve your skills.
• Understand the underlying concepts: Don't just memorize formulas and procedures. Take the time to understand the underlying mathematical concepts and principles.
• Seek help when needed: Don't be afraid to ask for help if you're struggling with simplifying expressions. Reach out to your teacher, a tutor, or a classmate for support.