Question

What are “like terms”? Why can we only add like terms?

13.)What is the closure property? What does it have to do with adding, subtracting, and multiplying polynomials?

Answer 1

Like terms are mathematical terms that contain the same variables. We combine like terms, because it simplifies algebraic expressions.

Closure property is the term for when you add or multiply two whole numbers together, and the result is always just a whole number. It is related to adding, subtracting, and multiplying polynomials, because when something is closed, the output will result in being the same type of object as the inputs.

Explanation:

Like terms: When combining like terms, we add their coefficients. For instance, if we have 3y and 4y, we get 7y. That is because we added (3+4) to get 7, and plugged in the variable "y".

Closure property: Adding, subtracting, or multiplying two polynomials will output a polynomial.

Answer 2

In algebra, like terms are coefficients containing the same variable. We can only add like terms because unlike terms don’t have the same variables. Because of this, not all variables and constants can be factored out to result with one expression. Monomials only are present when like terms are combined in terms of addition.

What is closure property? That’s a good question. Closure property is a method and idea used in math that often emphasizes the explanation that the sum of two whole numbers will always result in a whole number (that is what it has to do with addition). In subtraction, closure property states that the difference between two rational numbers (pi excluded) will always result in a rational number. When multiplying polynomials, the rule is that, like subtraction, the multiplication of two rational numbers always will end in a rational number.