Fact Check: Are xy and yx like terms?

Are xy and yx Like Terms?

Introduction

The claim under examination is whether the algebraic terms "xy" and "yx" are considered like terms. This question arises from the fundamental principles of algebra, particularly the definitions of like and unlike terms. Understanding this classification is essential for simplifying algebraic expressions correctly.

What We Know

1. Definition of Like Terms: Like terms are defined as terms that have the same variables raised to the same powers. The coefficients (numerical factors) can differ. For example, terms such as 2x and 3x are like terms because they both contain the variable x raised to the same power 19.

2. Commutative Property: The commutative property of multiplication states that the order of factors does not affect the product. Therefore, xy and yx represent the same product, as multiplication is commutative 39.

3. Examples of Like Terms: Various educational sources confirm that xy and yx are indeed like terms due to their identical variables and the application of the commutative property. For instance, BYJU'S states that xy and yx can be classified as like terms 4.

4. Contradictory Views: Some sources, such as the CK-12 Foundation, emphasize that terms must have the same literal factors to be classified as like terms. However, they do not specifically address the commutative property in the context of xy and yx 2.

Analysis

The claim that xy and yx are like terms is supported by several credible sources that discuss the properties of algebraic expressions.

• Credibility of Sources:

  • Math is Fun and SplashLearn provide clear definitions and examples of like terms, emphasizing that the order of multiplication does not matter 13. These sources are generally reliable for educational content, but they may lack peer-reviewed validation.
  • CK-12 Foundation is a reputable educational platform that offers a range of resources for students, although it does not directly address the commutative property in its explanation 2.
  • BYJU'S is a well-known educational technology company that provides learning resources, and its explanation aligns with the majority view on this topic 4.
  • TruthOrFake Blog presents a recent perspective on the claim, supporting the idea that xy and yx are like terms due to their shared variables and the commutative property 7. However, the blog's credibility may be questioned due to its informal nature and lack of academic rigor.

• Methodology and Evidence: The majority of sources rely on established mathematical principles, such as the commutative property, to support their claims. However, some sources may not provide comprehensive explanations or examples that could further clarify the concept for learners.

• Potential Bias: Educational websites often aim to simplify concepts for students, which can lead to oversimplification. Additionally, platforms like TruthOrFake may have an agenda to debunk misconceptions, which could influence their presentation of information.

Conclusion

Verdict: True

The claim that "xy" and "yx" are like terms is supported by the commutative property of multiplication, which states that the order of factors does not affect the product. This principle is widely recognized in algebra, and credible educational sources affirm that both terms share the same variables raised to the same powers, thus classifying them as like terms.

However, it is important to note that some sources, such as the CK-12 Foundation, emphasize a stricter interpretation of like terms that may not explicitly incorporate the commutative property. This highlights a potential nuance in the understanding of the term "like terms" that may vary among different educational contexts.

While the majority of evidence supports the classification of "xy" and "yx" as like terms, it is essential to acknowledge that educational interpretations can differ, and not all sources may provide a comprehensive view. Readers are encouraged to critically evaluate the information presented and consider multiple perspectives when forming their understanding of algebraic concepts.

Sources

1. Math is Fun - Like Terms: https://www.mathsisfun.com/algebra/like-terms.html
2. CK-12 Foundation - Are xy and yx considered like terms?: https://www.ck12.org/flexi/math-grade-6/simplify-variable-expressions-involving-addition-and-subtraction/are-xy-and-yx-considered-like-terms/
3. SplashLearn - Like and Unlike Algebraic Terms: https://www.splashlearn.com/math-vocabulary/like-and-unlike-algebraic-terms
4. BYJU'S - Steps to Use the Combine Like Terms Calculator: https://byjus.com/combine-like-terms-calculator/#:~:text=Are%20XY%20and%20YX%20like,be%20classified%20as%20like%20terms.
5. TruthOrFake Blog - Fact Check: Are YX and XY like terms?: https://truthorfake.com/blog/are-yx-and-xy-like-terms-9307
6. Math.com - Algebra Basics - Like terms: http://www.math.com/school/subject2/lessons/S2U2L4DP.html
7. Cambridge (CIE) IGCSE Maths Revision Notes: https://www.savemyexams.com/igcse/maths/cie/25/extended/revision-notes/algebra-and-sequences/algebra-toolkit/collecting-like-terms/