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.
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 [tex]5y{\text{ and }}7y.[/tex]
The sum of the two polynomials can be obtained as follows,
[tex]\begin{aligned}{\text{Sum}} &= 5y + 7y\\&= 12y\\\end{aligned}[/tex]
The sum of the two monomials is monomial.
Consider the two monomials as [tex]5y{\text{ and }}7x.[/tex]
The sum of the two polynomials can be obtained as follows,
[tex]{\text{Sum}} = 5y + 7x[/tex]
The sum of the two monomials is not monomial.
Consider the two monomials as [tex]4y{\text{ and }}6x.[/tex]
The product of the two polynomials can be obtained as follows,
[tex]\begin{aligned}{\text{Product}} &= 4y \times 6x\\&= 24xy\\\end{aligned}[/tex]
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.
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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.
