Simplify The Expression: { -8 + 4 + (-4s) + (-1) + (-7s)$}$

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for students and professionals alike. In this article, we will focus on simplifying a specific algebraic expression, which involves combining like terms and applying the rules of arithmetic operations. By the end of this article, you will have a clear understanding of how to simplify algebraic expressions and be able to apply this knowledge to a wide range of mathematical problems.

Understanding the Expression

The given expression is: ${-8 + 4 + (-4s) + (-1) + (-7s)}$

This expression consists of five terms, each of which is a combination of a constant and a variable (s). To simplify this expression, we need to combine like terms, which means combining terms that have the same variable raised to the same power.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this expression, we have two like terms: ${-4s}$ and ${-7s}$. These two terms have the same variable (s) raised to the same power (1).

To combine these like terms, we need to add their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficient of ${-4s}$ is -4, and the coefficient of ${-7s}$ is -7.

# Define the coefficients of the like terms
coefficient1 = -4
coefficient2 = -7
combined_coefficient = coefficient1 + coefficient2

The result of adding the coefficients is -11. Therefore, the combined like term is ${-11s}$.

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression by combining the constants and the variable terms.

The expression can be rewritten as: ${-8 + 4 + (-11s) + (-1)}$

We can combine the constants by adding them: ${-8 + 4 - 1 = -5}$

Therefore, the simplified expression is: ${-5 - 11s}$

Conclusion

Simplifying algebraic expressions is an essential skill for students and professionals alike. By combining like terms and applying the rules of arithmetic operations, we can simplify complex expressions and make them easier to work with. In this article, we have focused on simplifying a specific algebraic expression, which involves combining like terms and applying the rules of arithmetic operations. By following the steps outlined in this article, you will be able to simplify algebraic expressions and apply this knowledge to a wide range of mathematical problems.

Example Problems

1. Simplify the expression: ${2x + 3x + 4y - 2y}$
2. Simplify the expression: ${-5a + 2a + 3b - 2b}$
3. Simplify the expression: ${4x - 2x + 3y + 2y}$

Answer Key

1. ${5x + y}$
2. ${-3a + b}$
3. ${2x + 5y}$

Tips and Tricks

• When simplifying algebraic expressions, always start by combining like terms.
• Use the rules of arithmetic operations to combine constants and variables.
• Make sure to check your work by plugging in values for the variables and checking that the expression is true.
• Practice simplifying algebraic expressions regularly to build your skills and confidence.

Further Reading

• Algebraic Expressions: A Comprehensive Guide
• Simplifying Algebraic Expressions: A Step-by-Step Guide
• Algebraic Manipulations: A Guide to Simplifying Expressions

References

• [1] Algebraic Expressions: A Comprehensive Guide. (n.d.). Retrieved from https://www.example.com/algebraic-expressions
• [2] Simplifying Algebraic Expressions: A Step-by-Step Guide. (n.d.). Retrieved from https://www.example.com/simplifying-algebraic-expressions
• [3] Algebraic Manipulations: A Guide to Simplifying Expressions. (n.d.). Retrieved from https://www.example.com/algebraic-manipulations
  Frequently Asked Questions: Simplifying Algebraic Expressions ===========================================================

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

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

A: A variable is a symbol that represents a value that can change, while a constant is a value that remains the same.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms, which means combining terms that have the same variable raised to the same power. You can also use the rules of arithmetic operations to combine constants and variables.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 2x and 3x are like terms because they both have the variable x raised to the power of 1.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract their coefficients. The coefficient of a term is the number that is multiplied by the variable.

Q: What is the coefficient of a term?

A: The coefficient of a term is the number that is multiplied by the variable. For example, in the term 2x, the coefficient is 2.

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

A: To simplify an expression with multiple variables, you need to combine like terms for each variable separately. For example, if you have the expression 2x + 3y + 4x, you can combine the like terms for x by adding 2 and 4, resulting in 6x.

Q: Can I simplify an expression with negative coefficients?

A: Yes, you can simplify an expression with negative coefficients by following the same rules as for positive coefficients. For example, if you have the expression -2x + 3y - 4x, you can combine the like terms for x by adding -2 and -4, resulting in -6x.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to evaluate the expression inside the parentheses first. Then, you can simplify the expression by combining like terms.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions by following the same rules as for whole numbers. For example, if you have the expression 1/2x + 3/4y, you can combine the like terms for x by adding 1/2 and 3/4, resulting in 5/4x.

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

A: To check your work, you can plug in values for the variables and check that the expression is true. For example, if you have the expression 2x + 3y and you plug in x = 1 and y = 2, you should get 5 as the result.

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

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

• Not combining like terms
• Not following the order of operations
• Not checking your work
• Not using the correct rules for arithmetic operations

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through examples and exercises in a textbook or online resource. You can also try simplifying expressions on your own and checking your work to make sure you are getting the correct results.