Question

Is the sum of two monomials always a monomial? Is their product always a monomial?

Answer 1

The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.

Further explanation:

Explanation:

Consider the two monomials as $5y{\text{ and }}7y.$

The sum of the two polynomials can be obtained as follows,

$\begin{aligned}{\text{Sum}} &= 5y + 7y\\&= 12y\\\end{aligned}$

The sum of the two monomials is monomial.

Consider the two monomials as $5y{\text{ and }}7x.$

The sum of the two polynomials can be obtained as follows,

${\text{Sum}} = 5y + 7x$

The sum of the two monomials is not monomial.

Consider the two monomials as $4y{\text{ and }}6x.$

The product of the two polynomials can be obtained as follows,

$\begin{aligned}{\text{Product}} &= 4y \times 6x\\&= 24xy\\\end{aligned}$

The product of the two monomials is monomial.

The sum of two monomials is not always a monomial and the product of two monomials is always a monomial.

Learn more

1. Learn more about the polynomial brainly.com/question/12996944
2. Learn more about logarithm model brainly.com/question/13005829
3. Learn more about the product of binomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: sum, two monomial, monomials, always monomial, product, always, monomial, factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.

Answer 2

Sum of two monomials is not necessarily always a monomial.

For example:

Suppose we have two monomials as 2x and 5x.

Adding 2x+5x , we get 7x.

So if two monomials are both like terms then their sum will be a monomial.

Suppose we have two monomials as 3y and 4x

Now these are both monomials but unlike, so we cannot add them together and sum would be 3y + 4x , which is a binomial.

So if we have like terms then the sum is monomial but if we have unlike terms sum is binomial.

Product of monomials:

suppose we have 2x and 5y,

Product : 2x*5y = 10xy ( which is a monomial)

So yes product of two monomials is always a monomial.