Question

The coefficient of the product of two monomials is not equal to the product of their coefficient.
A) True
B) False
C) Ambiguous
D) Data insufficient

Answer 1

Hint: As monomials contain only a single term, we can consider two random monomials and then will multiply them. We will compare the coefficient of the product of monomials with the product of their coefficients, and then we will get the answer.

Complete step by step solution:
Monomials are the algebraic expressions containing a single term.
Consider two arbitrary monomials as $ax$ and $by$ where a and b are arbitrary real numbers.
Coefficient of $ax$ is a.
Coefficient of $by$ is b.
Now, as per the question statement, the coefficient of the product of two monomials is not equal to the product of their coefficient,
We have to first calculate the product of the two monomials, and then compare it to the product of their coefficient.
Product of two polynomials is $ax \times by$.
Product of two polynomials is: $abxy$
Now, $abxy$ is also a monomial as the number of terms in the expression is 1.
So, Coefficient of $abxy$ is $ab$ …(i)
Now, we will calculate the product of the coefficients of monomials $ax$ and $by$,
It will be: $a \times b = ab$ …(ii)
From (i) and (ii), we get
Coefficient of $abxy$ is equal to the product of the coefficients of monomials $ax$ and $by$
Thus, the coefficient of the product of two monomials is equal to the product of their coefficient.
Hence, the given statement “The coefficient of the product of two monomials is not equal to the product of their coefficient” is false, so the correct answer is option B.

Note: Students must know the meaning of polynomial and how to identify its coefficient. A polynomial is an algebraic expression containing the multiple numbers of terms with the number of variables. As a polynomial has multiple terms, the coefficient of each term is different. We have to first identify the term and then collect the number part (or without variable part) to get the coefficient of a term of a polynomial.