Question

Which among the following pairs of terms have different literal factors?

• A. $10pq,20pq$
• B. $256ab,562ba$
• C. $81mn,96m^2{n}^2$
• D. $786rs,144rs$

Answer 1

The correct option is C $81mn,96m^2{n}^2$

$\underset{–}{\text{Literal Factor:}}$
Literal factor is a part of an algebraic term without the constant.
For example, $\underset{–}{2x^{2}y}$ and $\underset{–}{5y}$ have literal factors as $\underset{–}{x^{2}y}$ and $\underset{–}{y}$ respectively.

Now, let's take a look at each pair of terms one-by-one.

$\bullet$ (a.) $\underset{–}{10pq,20pq:}$
Both the terms have the same literal factor as $\underset{–}{pq}$.

$\bullet$ (b.) $\underset{–}{256ab,562ba:}$
Both the terms have the same literal factor as $\underset{–}{ab}$.
($\because ab=ba;$ Multiplication is commutative)

$\bullet$ (c.) $\underset{–}{81mn,96m^2{n}^2:}$
Both the terms have different literal factors. $\underset{–}{81mn}$ has literal factor as $\underset{–}{mn}$ and $\underset{–}{96m^2{n}^2}$ has literal factor as $\underset{–}{m^2{n}^2}.$

$\bullet$ (d.) $\underset{–}{786rs,144rs:}$
Both the terms have the same literal factor as $\underset{–}{rs}$.

Therefore, option (c.) is the correct answer.