# Understand Polynomial Terms: Like & Unlike Terms

• MHB
• PeekaTweak
In summary, a like term in set theory can be compared to similar terms in polynomials. It refers to terms that appear in both sets, just like how the term 'x' appears in both polynomials 3x^2 + 2x - 3 and 5x^3 - 3x + 7. This concept is not limited to polynomials and can be applied to sets as well. As an high-school student, the listener is looking for an explanation of like terms and unlike terms in set theory. The explanation does not have to be lengthy, as long as it provides a clear understanding from their point of view.
PeekaTweak
I would like to have someone who would be willing to explain me what is a like term and an unlike term in terms of set theory. I'm just an high-scool student, but I really would like to understand it from that point of view anyway. It doesn't have to be a 1000 pages long of explanations.

PeekaTweak said:
I would like to have someone who would be willing to explain me what is a like term and an unlike term in terms of set theory. I'm just an high-scool student, but I really would like to understand it from that point of view anyway. It doesn't have to be a 1000 pages long of explanations.
In terms of polynomials (I can't think of how to applied this to sets) a "like" term is a comparison between two terms of the polynomial. For example, consider the two polynomials $$\displaystyle 3x^2 + 2x - 3$$ and $$\displaystyle 5x^3 - 3x + 7$$. The like terms are the terms that are in both polynomials. Here the there is only one like term: the one in x. (I suppose you could call the constant terms "like" as they are both terms in $$\displaystyle x^0$$ but I don't think anyone does this.)

-Dan

## 1. What are polynomial terms?

Polynomial terms are expressions that consist of variables and coefficients, connected by mathematical operations such as addition, subtraction, multiplication, and division. These terms are used to represent mathematical relationships and can have different degrees depending on the highest exponent of the variable.

## 2. What is the difference between like and unlike terms?

Like terms are polynomial terms that have the same variables raised to the same power. Unlike terms, on the other hand, have different variables or different powers of the same variable. For example, 2x and 5x are like terms since they both have the variable x raised to the first power, while 2x and 2x^2 are unlike terms.

## 3. How do you simplify polynomial expressions?

To simplify polynomial expressions, you need to combine like terms. First, identify the like terms by looking at the variables and their powers. Then, combine the coefficients of the like terms by performing the indicated mathematical operations. Finally, write the simplified expression using the combined coefficients and the common variables.

## 4. Can unlike terms be combined?

No, unlike terms cannot be combined. This is because they have different variables or different powers of the same variable, making them mathematically different. For example, 2x and 2y cannot be combined since they have different variables, and 2x and 2x^2 cannot be combined since they have different powers of x.

## 5. Why is it important to understand polynomial terms?

Understanding polynomial terms is essential because they are the building blocks of algebraic expressions and equations. They allow us to represent mathematical relationships and solve problems in various fields, including science, engineering, and economics. Additionally, understanding polynomial terms is crucial for simplifying expressions, solving equations, and graphing functions.

Replies
6
Views
1K
Replies
1
Views
1K
Replies
9
Views
2K
Replies
1
Views
1K
Replies
8
Views
2K
Replies
10
Views
3K
Replies
76
Views
5K
Replies
1
Views
2K
Replies
7
Views
2K
Replies
45
Views
4K