Forgetting to distribute the negative sign

Oct 13, 2025 by miodeya.com 69 views

Introduction

Algebraic expressions are a fundamental concept in mathematics, and simplifying them is an essential skill for any math enthusiast. In this article, we will explore the process of simplifying algebraic expressions, focusing on the addition of two or more expressions. We will use the given expression as an example to demonstrate the step-by-step process.

The Given Expression

The given expression is:

\left(-9u^3 + 5u^2 + 7u - 8\right) + \left(-4u^3 - 6u^2 - 8u - 2\right)

Step 1: Distribute the Negative Sign

To simplify the expression, we need to distribute the negative sign to each term inside the second parentheses.

\left(-9u^3 + 5u^2 + 7u - 8\right) + \left(-4u^3 - 6u^2 - 8u - 2\right)

= \left(-9u^3 + 5u^2 + 7u - 8\right) - 4u^3 - 6u^2 - 8u - 2

Step 2: Combine Like Terms

Now, we need to combine like terms, which means combining terms with the same variable and exponent.

= -9u^3 - 4u^3 + 5u^2 - 6u^2 + 7u - 8u - 8 - 2

Step 3: Simplify the Expression

Next, we need to simplify the expression by combining the like terms.

= -13u^3 - u^2 - u - 10

Conclusion

In this article, we have demonstrated the process of simplifying algebraic expressions by adding two or more expressions. We have used the given expression as an example to illustrate the step-by-step process. By following these steps, you can simplify any algebraic expression and make it easier to work with.

Tips and Tricks

When simplifying algebraic expressions, always start by distributing the negative sign to each term inside the second parentheses.
Next, combine like terms by adding or subtracting the coefficients of the same variable and exponent.
Finally, simplify the expression by combining the like terms.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

Physics and Engineering: Algebraic expressions are used to describe the motion of objects, forces, and energies.
Computer Science: Algebraic expressions are used to represent algorithms and data structures.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Common Mistakes

When simplifying algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

Forgetting to distribute the negative sign: Make sure to distribute the negative sign to each term inside the second parentheses.
Not combining like terms: Make sure to combine like terms by adding or subtracting the coefficients of the same variable and exponent.
Not simplifying the expression: Make sure to simplify the expression by combining the like terms.

Conclusion

Introduction

In our previous article, we explored the process of simplifying algebraic expressions by adding two or more expressions. In this article, we will answer some frequently asked questions about 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 to represent a mathematical relationship between variables and constants.

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

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations, while an equation is a statement that says two expressions are equal. For example, 2x + 3 is an algebraic expression, while 2x + 3 = 5 is an equation.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to follow these steps:

Distribute the negative sign to each term inside the second parentheses.
Combine like terms by adding or subtracting the coefficients of the same variable and exponent.
Simplify the expression by combining the like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, 2x and 4x are like terms, while 2x and 3y are not like terms.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the same variable and exponent. For example, 2x + 4x = 6x, while 2x - 4x = -2x.

Q: What is the order of operations?

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

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate expressions with exponents next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate addition and subtraction operations from left to right.

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to follow these steps:

Evaluate the expression inside the parentheses first.
Simplify the expression by combining like terms.
Finally, simplify the expression by combining the like terms.

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

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

Forgetting to distribute the negative sign.
Not combining like terms.
Not simplifying the expression.
Not following the order of operations.

Conclusion

In conclusion, simplifying algebraic expressions is an essential skill for any math enthusiast. By following the step-by-step process outlined in this article, you can simplify any algebraic expression and make it easier to work with. Remember to distribute the negative sign, combine like terms, and simplify the expression to get the final result.

Tips and Tricks

When simplifying algebraic expressions, always start by distributing the negative sign to each term inside the second parentheses.
Next, combine like terms by adding or subtracting the coefficients of the same variable and exponent.
Finally, simplify the expression by combining the like terms.

Real-World Applications

Simplifying algebraic expressions has many real-world applications, including:

Physics and Engineering: Algebraic expressions are used to describe the motion of objects, forces, and energies.
Computer Science: Algebraic expressions are used to represent algorithms and data structures.
Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Common Mistakes

When simplifying algebraic expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

Forgetting to distribute the negative sign: Make sure to distribute the negative sign to each term inside the second parentheses.
Not combining like terms: Make sure to combine like terms by adding or subtracting the coefficients of the same variable and exponent.
Not simplifying the expression: Make sure to simplify the expression by combining the like terms.