Indicate Whether The Terms Are Like Or Unlike.The Two Terms $5z^2$ And $-7z^2$ Are $\square$.

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Understanding Like and Unlike Terms in Algebra

In algebra, like terms are expressions that have the same variable(s) raised to the same power. Unlike terms, on the other hand, are expressions that have different variables or variables raised to different powers. In this discussion, we will examine whether the terms $5z^2$ and $-7z^2$ are like or unlike.

What are Like Terms?

Like terms are expressions that have the same variable(s) raised to the same power. For example, $2x^2$ and $5x^2$ are like terms because they both have the variable $x$ raised to the power of 2. Similarly, $3y^2$ and $-4y^2$ are like terms because they both have the variable $y$ raised to the power of 2.

What are Unlike Terms?

Unlike terms, on the other hand, are expressions that have different variables or variables raised to different powers. For example, $2x^2$ and $3y^2$ are unlike terms because they have different variables ($x$ and $y$). Similarly, $2x^2$ and $-4x^3$ are unlike terms because they have the same variable ($x$) but different powers (2 and 3).

Are $5z^2$ and $-7z^2$ Like or Unlike Terms?

Now that we have a clear understanding of like and unlike terms, let's examine whether $5z^2$ and $-7z^2$ are like or unlike. At first glance, it may seem like they are unlike terms because they have different coefficients (5 and -7). However, upon closer inspection, we can see that they both have the same variable ($z$) raised to the same power (2).

Conclusion

Based on our analysis, we can conclude that $5z^2$ and $-7z^2$ are like terms. They have the same variable ($z$) raised to the same power (2), which meets the definition of like terms.

Examples of Like and Unlike Terms

To further illustrate the concept of like and unlike terms, let's consider some examples:

  • Like terms: $2x^2$ and $5x^2$, $3y^2$ and $-4y^2$
  • Unlike terms: $2x^2$ and $3y^2$, $2x^2$ and $-4x^3$

Simplifying Expressions with Like Terms

When simplifying expressions with like terms, we can combine the coefficients of the like terms. For example, if we have the expression $2x^2 + 5x^2$, we can combine the coefficients to get $7x^2$.

Real-World Applications of Like and Unlike Terms

Understanding like and unlike terms is crucial in algebra and other branches of mathematics. It helps us to simplify expressions, solve equations, and perform various mathematical operations. In real-world applications, like and unlike terms are used in physics, engineering, economics, and other fields to model and analyze complex systems.

Conclusion

In conclusion, like terms are expressions that have the same variable(s) raised to the same power, while unlike terms are expressions that have different variables or variables raised to different powers. The terms $5z^2$ and $-7z^2$ are like terms because they have the same variable ($z$) raised to the same power (2). Understanding like and unlike terms is essential in algebra and other branches of mathematics, and it has numerous real-world applications.

Key Takeaways

  • Like terms have the same variable(s) raised to the same power.
  • Unlike terms have different variables or variables raised to different powers.
  • The terms $5z^2$ and $-7z^2$ are like terms because they have the same variable ($z$) raised to the same power (2).
  • Understanding like and unlike terms is crucial in algebra and other branches of mathematics.
  • Like and unlike terms have numerous real-world applications in physics, engineering, economics, and other fields.
    Frequently Asked Questions (FAQs) about Like and Unlike Terms ====================================================================

Q: What are like terms in algebra?

A: Like terms are expressions that have the same variable(s) raised to the same power. For example, $2x^2$ and $5x^2$ are like terms because they both have the variable $x$ raised to the power of 2.

Q: What are unlike terms in algebra?

A: Unlike terms are expressions that have different variables or variables raised to different powers. For example, $2x^2$ and $3y^2$ are unlike terms because they have different variables ($x$ and $y$).

Q: How do I determine if two terms are like or unlike?

A: To determine if two terms are like or unlike, look at the variables and their powers. If the variables and powers are the same, the terms are like. If the variables or powers are different, the terms are unlike.

Q: Can like terms have different coefficients?

A: Yes, like terms can have different coefficients. For example, $2x^2$ and $5x^2$ are like terms because they both have the variable $x$ raised to the power of 2, even though they have different coefficients (2 and 5).

Q: Can unlike terms have the same variable?

A: Yes, unlike terms can have the same variable, but with different powers. For example, $2x^2$ and $3x^3$ are unlike terms because they have the same variable ($x$), but different powers (2 and 3).

Q: How do I simplify expressions with like terms?

A: To simplify expressions with like terms, combine the coefficients of the like terms. For example, if we have the expression $2x^2 + 5x^2$, we can combine the coefficients to get $7x^2$.

Q: What are some real-world applications of like and unlike terms?

A: Like and unlike terms have numerous real-world applications in physics, engineering, economics, and other fields. For example, in physics, like and unlike terms are used to model and analyze complex systems, such as the motion of objects and the behavior of electrical circuits.

Q: Why is it important to understand like and unlike terms?

A: Understanding like and unlike terms is crucial in algebra and other branches of mathematics. It helps us to simplify expressions, solve equations, and perform various mathematical operations. In real-world applications, like and unlike terms are used to model and analyze complex systems.

Q: Can you provide more examples of like and unlike terms?

A: Here are some more examples:

  • Like terms: $2x^2$ and $5x^2$, $3y^2$ and $-4y^2$
  • Unlike terms: $2x^2$ and $3y^2$, $2x^2$ and $-4x^3$
  • Like terms with different coefficients: $2x^2$ and $5x^2$, $3y^2$ and $-4y^2$
  • Unlike terms with the same variable: $2x^2$ and $3x^3$, $2y^2$ and $-4y^2$

Conclusion

In conclusion, like and unlike terms are fundamental concepts in algebra and other branches of mathematics. Understanding like and unlike terms is crucial in simplifying expressions, solving equations, and performing various mathematical operations. We hope this FAQ article has provided you with a better understanding of like and unlike terms and their real-world applications.