Question

Identify the unlike term in the following: $2{{a}^{2}}x,2ax,x2{{a}^{2}},{{a}^{2}}x2,4{{a}^{2}}2x$.

Answer 1

Hint: We first complete the multiplication for the variables and the constants if possible. We find their simplified forms. We first equate the variables and find the unlike terms. If they are all equal variables wise then we compare the constants to find the unlike terms.

Complete step-by-step solution:
There are in total five representations of the multiplications.
We complete the multiplication of the variables and the constants if possible and then find its simplified form.
We take $2{{a}^{2}}x$ and find that the term is already in its simplified form.
We now take $2ax$ and find that the term is also in its simplified form.
Now for $x2{{a}^{2}}$, we simplify to get $2{{a}^{2}}x$.
For ${{a}^{2}}x2$, we simplify to get $2{{a}^{2}}x$.
For $4{{a}^{2}}2x$, we first multiply the constants $4\times 2=8$ and then simplify to get $8{{a}^{2}}x$
Now we have to find the unlike terms.
The main variables part for four of the given terms are equal to ${{a}^{2}}x$.
The only case where it was different is $2ax$.
Therefore, the unlike term among $2{{a}^{2}}x,2ax,x2{{a}^{2}},{{a}^{2}}x2,4{{a}^{2}}2x$ is $2ax$.

Note: The comparison of the terms will be considered based on the variables where we first compare the variables. The comparison of the constants will be taken into consideration if the total power value of the variables is equal.