Simplify The Expression:${ -5x^5 - 4x^5 \times (-3) }$

Mar 12, 2025 by ADMIN 56 views

Simplify the Expression: A Step-by-Step Guide to Combining Like Terms

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities more efficiently. One of the most common techniques used to simplify expressions is combining like terms. In this article, we will focus on simplifying the given expression: $-5x^5 - 4x^5 \times (-3)$ . We will break down the steps involved in simplifying this expression and provide a clear explanation of each step.

Understanding Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, we have two terms: $-5x^5$ and $-4x^5 \times (-3)$ . Both terms have the same variable, $x$ , raised to the same power, $5$ . Therefore, they are like terms.

Distributing the Negative Sign

The second term in the expression is $-4x^5 \times (-3)$ . When we multiply two negative numbers, we get a positive result. Therefore, $-4x^5 \times (-3) = 12x^5$ .

Combining Like Terms

Now that we have simplified the second term, we can combine the two like terms: $-5x^5$ and $12x^5$ . To combine like terms, we add their coefficients (the numbers in front of the variable). In this case, we add $-5$ and $12$ .

Simplifying the Expression

When we add $-5$ and $12$ , we get $7$ . Therefore, the simplified expression is $7x^5$ .

Conclusion

In this article, we simplified the given expression by combining like terms. We started by identifying the like terms in the expression, then distributed the negative sign in the second term, and finally combined the like terms by adding their coefficients. The simplified expression is $7x^5$ .

Tips and Tricks

When simplifying expressions, always look for like terms.
Distribute the negative sign when multiplying two negative numbers.
Combine like terms by adding their coefficients.

Common Mistakes to Avoid

Not identifying like terms in an expression.
Not distributing the negative sign when multiplying two negative numbers.
Not combining like terms by adding their coefficients.

Real-World Applications

Simplifying expressions is a crucial skill in many real-world applications, including:

Physics: Simplifying expressions is essential in physics to solve equations and inequalities related to motion, energy, and momentum.
Engineering: Simplifying expressions is critical in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
Computer Science: Simplifying expressions is essential in computer science to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities more efficiently. By combining like terms, we can simplify expressions and make them easier to work with. In this article, we simplified the given expression by combining like terms and provided a clear explanation of each step. We also discussed common mistakes to avoid and real-world applications of simplifying expressions.

Frequently Asked Questions

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power.

Q: How do I distribute the negative sign?

A: When multiplying two negative numbers, we get a positive result.

Q: How do I combine like terms?

A: To combine like terms, we add their coefficients (the numbers in front of the variable).

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

A: Not identifying like terms, not distributing the negative sign, and not combining like terms by adding their coefficients.

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions is essential in physics, engineering, and computer science to solve equations and inequalities, design and optimize systems, and optimize algorithms and data structures.

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Introduction

In our previous article, we discussed how to simplify the expression $-5x^5 - 4x^5 \times (-3)$ by combining like terms. In this article, we will provide a Q&A guide to help you understand the concept of combining like terms and simplify expressions.

Q&A

Q: What are like terms?

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

Q: How do I identify like terms in an expression?

A: To identify like terms, look for terms that have the same variable raised to the same power. For example, in the expression $2x^2 + 3x^2 + 4x^3$ , the like terms are $2x^2$ and $3x^2$ because they have the same variable, $x$ , raised to the same power, $2$ .

Q: What is the rule for combining like terms?

A: The rule for combining like terms is to add their coefficients (the numbers in front of the variable). For example, if we have the expression $2x^2 + 3x^2$ , we can combine the like terms by adding their coefficients: $2 + 3 = 5$ . Therefore, the simplified expression is $5x^2$ .

Q: How do I distribute the negative sign when multiplying two negative numbers?

A: When multiplying two negative numbers, we get a positive result. For example, $-2 \times -3 = 6$ . Therefore, when we have an expression like $-4x^5 \times (-3)$ , we can simplify it by distributing the negative sign: $-4x^5 \times (-3) = 12x^5$ .

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

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

Not identifying like terms in an expression.
Not distributing the negative sign when multiplying two negative numbers.
Not combining like terms by adding their coefficients.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, follow these steps:

Identify the like terms in the expression.
Distribute the negative sign when multiplying two negative numbers.
Combine the like terms by adding their coefficients.

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions is essential in many real-world applications, including:

Physics: Simplifying expressions is critical in physics to solve equations and inequalities related to motion, energy, and momentum.
Engineering: Simplifying expressions is essential in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
Computer Science: Simplifying expressions is critical in computer science to optimize algorithms and data structures.

Tips and Tricks

Always look for like terms in an expression.
Distribute the negative sign when multiplying two negative numbers.
Combine like terms by adding their coefficients.
Simplify expressions step by step to avoid mistakes.

Common Mistakes to Avoid

Not identifying like terms in an expression.
Not distributing the negative sign when multiplying two negative numbers.
Not combining like terms by adding their coefficients.

Real-World Applications

Simplifying expressions is a crucial skill in many real-world applications, including:

Physics: Simplifying expressions is critical in physics to solve equations and inequalities related to motion, energy, and momentum.
Engineering: Simplifying expressions is essential in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
Computer Science: Simplifying expressions is critical in computer science to optimize algorithms and data structures.

Final Thoughts

Simplifying expressions is a fundamental skill in algebra that helps us solve equations and inequalities more efficiently. By combining like terms, we can simplify expressions and make them easier to work with. In this article, we provided a Q&A guide to help you understand the concept of combining like terms and simplify expressions.

Frequently Asked Questions

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

A: Some common mistakes to avoid when simplifying expressions include not identifying like terms, not distributing the negative sign, and not combining like terms by adding their coefficients.

Q: How do I simplify an expression with multiple like terms?

A: To simplify an expression with multiple like terms, follow these steps: identify the like terms, distribute the negative sign, and combine the like terms by adding their coefficients.

Q: What are some real-world applications of simplifying expressions?

A: Simplifying expressions is essential in physics, engineering, and computer science to solve equations and inequalities, design and optimize systems, and optimize algorithms and data structures.

Q: How do I distribute the negative sign when multiplying two negative numbers?

A: When multiplying two negative numbers, we get a positive result. For example, $-2 \times -3 = 6$ .