Simplify The Expression:$3y^2z - 24x^2y^3z + 16x^2y^3z^3$

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. It involves combining like terms and eliminating any unnecessary components. In this article, we will simplify the given expression: $3y^2z - 24x^2y^3z + 16x^2y^3z^3$. We will break down the process into manageable steps, making it easy to understand and follow.

Step 1: Identify Like Terms

Like terms are terms that have the same variable(s) raised to the same power. In the given expression, we can identify the following like terms:

• $3y^2z$
• $-24x^2y^3z$
• $16x^2y^3z^3$

However, we notice that the first two terms have the same variable(s) raised to the same power, while the third term has an additional variable $z^3$. Therefore, we cannot combine the first two terms with the third term.

Step 2: Combine Like Terms

Now, let's combine the first two like terms:

$3y^2z - 24x^2y^3z$

We can factor out the common term $-3y^2z$ from both terms:

$-3y^2z(8x^2y - 1)$

Step 3: Simplify the Expression

Now that we have combined the like terms, we can simplify the expression by multiplying the remaining terms:

$-3y^2z(8x^2y - 1) + 16x^2y^3z^3$

We can distribute the negative sign to the terms inside the parentheses:

$-24x^2y^3z + 3y^2z + 16x^2y^3z^3$

Now, we can combine the like terms again:

$-24x^2y^3z + 16x^2y^3z^3 + 3y^2z$

We can factor out the common term $-8x^2y^3$ from the first two terms:

$-8x^2y^3z(3 - 2z^2) + 3y^2z$

Step 4: Final Simplification

Now that we have simplified the expression, we can write the final answer:

$-8x^2y^3z(3 - 2z^2) + 3y^2z$

This is the simplified expression.

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and inequalities. By identifying like terms, combining them, and simplifying the expression, we can arrive at the final answer. In this article, we simplified the given expression: $3y^2z - 24x^2y^3z + 16x^2y^3z^3$. We hope this step-by-step guide has helped you understand the process of simplifying expressions.

Common Mistakes to Avoid

When simplifying expressions, it's essential to avoid common mistakes. Here are a few:

• Not identifying like terms
• Not combining like terms
• Not distributing the negative sign correctly
• Not factoring out common terms

By avoiding these mistakes, you can ensure that your simplified expression is accurate and correct.

Real-World Applications

Simplifying expressions has numerous real-world applications. Here are a few:

• Physics: Simplifying expressions is crucial in physics, where we often deal with complex equations and inequalities. By simplifying expressions, we can arrive at the final answer and understand the underlying physics.
• Engineering: Simplifying expressions is also essential in engineering, where we often deal with complex systems and equations. By simplifying expressions, we can design and optimize systems more efficiently.
• Computer Science: Simplifying expressions is also used in computer science, where we often deal with complex algorithms and equations. By simplifying expressions, we can optimize algorithms and improve performance.

Final Thoughts

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Introduction

In our previous article, we simplified the expression: $3y^2z - 24x^2y^3z + 16x^2y^3z^3$. We broke down the process into manageable steps, making it easy to understand and follow. In this article, we will answer some frequently asked questions (FAQs) related to simplifying expressions.

Q: What are like terms?

A: Like terms are terms that have the same variable(s) raised to the same power. For example, in the expression $3y^2z - 24x^2y^3z + 16x^2y^3z^3$, the terms $3y^2z$ and $-24x^2y^3z$ are like terms because they have the same variable(s) raised to the same power.

Q: How do I identify like terms?

A: To identify like terms, you need to look for terms that have the same variable(s) raised to the same power. You can do this by comparing the coefficients and variables of each term.

Q: What is the difference between combining like terms and simplifying an expression?

A: Combining like terms involves adding or subtracting terms that have the same variable(s) raised to the same power. Simplifying an expression involves combining like terms and eliminating any unnecessary components.

Q: Can I simplify an expression by just combining like terms?

A: No, you cannot simplify an expression by just combining like terms. You need to eliminate any unnecessary components and simplify the expression further.

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 combining like terms
• Not distributing the negative sign correctly
• Not factoring out common terms

Q: How do I distribute the negative sign correctly?

A: To distribute the negative sign correctly, you need to multiply the negative sign by each term inside the parentheses. For example, in the expression $-3y^2z(8x^2y - 1)$, you would multiply the negative sign by each term inside the parentheses: $-3y^2z(8x^2y) + 3y^2z(1)$.

Q: Can I simplify an expression with variables raised to different powers?

A: Yes, you can simplify an expression with variables raised to different powers. However, you need to be careful when combining like terms and eliminating any unnecessary components.

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

A: Some real-world applications of simplifying expressions include:

• Physics: Simplifying expressions is crucial in physics, where we often deal with complex equations and inequalities. By simplifying expressions, we can arrive at the final answer and understand the underlying physics.
• Engineering: Simplifying expressions is also essential in engineering, where we often deal with complex systems and equations. By simplifying expressions, we can design and optimize systems more efficiently.
• Computer Science: Simplifying expressions is also used in computer science, where we often deal with complex algorithms and equations. By simplifying expressions, we can optimize algorithms and improve performance.

Q: How can I practice simplifying expressions?

A: You can practice simplifying expressions by working through examples and exercises. You can also use online resources and tools to help you practice and improve your skills.

Conclusion

Simplifying expressions is a crucial skill in algebra that helps us solve equations and inequalities. By identifying like terms, combining them, and simplifying the expression, we can arrive at the final answer. In this article, we answered some frequently asked questions (FAQs) related to simplifying expressions. We hope this Q&A guide has helped you understand the process of simplifying expressions and has provided you with the confidence to tackle more complex expressions.