Question

State whether the following pair of terms is like or unlike:
$4{m^2}p$ and $4m{p^2}$

Answer 1

Hint: We will first decipher the definition of both like terms and unlike terms. After that, just check with the pair if they follow the criteria of like terms or unlike terms. Then, we will have our answer. For example: 4a and 20a are like terms but 7a and 20b are unlike terms.

Complete step-by-step answer:
Let us first write the definitions of like terms:
Like Terms: The terms that have the same variables and powers. The coefficients do not need to match. These are known as terms.
Example: $x$ and $7x$ are like because both the terms have power of $x$ as 1.
Now, let us write the definition of unlike terms:
Unlike Terms: The two or more terms that are not like terms, that is they do not have the same variables or powers. These terms are known as Unlike terms.
Example: $5{x^2}$ and $7xy$ are unlike terms because in $5{x^2}$, $x$ has a power of 2 and $y$ has a power of 0 whereas in $7xy$, $x$ has a power of 1 and $y$ has a power of 1.
Now coming to our question, 4m$^2$p and 4mp$^2$ are the given two terms.
In $4{m^2}p$, $m$ has a power of 2 and $p$ has a power of 1.
In $4m{p^2}$, $m$ has a power of 1 and $p$ has a power of 2.
Hence, these both terms are unlike.
Hence, $4{m^2}p$ and $4m{p^2}$ are unlike terms.

Note: Remember all the definitions used in solving the given question that is of Like and Unlike terms.
Check the powers of individually are the variables carefully and do now sum all the powers of variables but check individually. Because in both of the monomials combined power of $m$ and $p$ is 3. So, we might think of them as like.
We might do that these both monomials have $m$ and $p$ in them, so we consider them as like, but we need to carefully observe all the distinct variables.