Question

Find the following pairs: $6n,3m$
$\begin{align}
  & \text{(a)18mm} \\
 & \text{(b)9mn} \\
 & \text{(c)28mn} \\
 & \text{(d)none}\,\text{of}\,\text{these} \\
\end{align}$

Answer 1

Hint: Take the product of constant terms i.e. $\text{6}\,\text{and}\,\text{3}$ separately and the products of variables m and n separately. Now multiply the resultant of the two products considered at the initial step to get the correct answer.

Complete step by step answer:
Here we have been provided with a pair of monomials: \[6n,3n\] and we are asked to find their products. But first let us understand the meaning of the term monomial.
Now, monomial is an expression that contains only one term. For example: $a,6n,5x,9{{y}^{2}},10{{a}^{3}}{{b}^{2}}{{c}^{5}}$ etc. these are all examples of monomials as they contain only one term. A monomial converts into a binomial when the variables are separated with a (=) or (-) sign.
So. Let us come to the question. We have two monomials $6n\,\text{ and }3m$. So, taking their product, we get, $\Leftarrow 6n\times 3m=(6\times 3)\times (m\times n)$
Considering the products of constants separately and that of the variables separately, we get,
$\begin{align}
  & 6n\times 3m=18\times mn \\
 & 6n\times 3m=18mn \\
\end{align}$

So, the correct answer is “Option a”.

Note: One may note that we can find the correct option by another method also. What we will do is we will assign some values to m and n (say m=n=1) and then find the product of $6n$and $3m$. Now we will substitute the same values of m and n in options and find the respective products. Whichever option will match with the initially obtained products will be the answer. You must remember the formulas of exponents and power as it will be required if we will be given to find the product of terms like $a{{x}^{m}}\,and\,{{b}^{n}}$