Similarity of 7xy and -5yx

Similar terms in algebraic expressions have the same variables raised to the same powers. Let's analyze if 7xy and -5yx are similar terms.

Explanation

When we look at the two terms, 7xy and -5yx, we can see that they have the same variables (x and y), but in a different order. However, the order of the variables does not affect their similarity. To determine if they are similar terms, we need to check if they have the same powers.

Variables and Powers

In the term 7xy, the variable x has an implied power of 1, and the variable y also has an implied power of 1. Therefore, the powers of both x and y in 7xy are 1.

Similarly, in the term -5yx, the variable y has an implied power of 1, and the variable x has an implied power of 1. Thus, the powers of y and x in -5yx are also 1.

Conclusion

Since both 7xy and -5yx have the same variables (x and y) raised to the same powers (1), they are indeed similar terms. The only difference between the two terms is the order of the variables, which does not affect their similarity.

Summary

- Similar terms in algebraic expressions have the same variables raised to the same powers.
- The terms 7xy and -5yx are similar terms because they have the same variables (x and y) raised to the same powers (1).
- The order of the variables does not affect their similarity.
- Therefore, 7xy and -5yx are similar terms.

Yes