Question

Which among the following is/are not like terms to $9x^2$?

• A. $3x$
• B. $81x^2$
• C. $99x^2$
• D. $729x^3$

Answer 1

Answer: (A), (D)

$729x^3$

$\underset{–}{\text{Like Terms:}}$
Like terms in algebra are the terms which contain the same variables raised to the same power (or exponent).

Given term: $9x^2$
$\bullet$ Variable is $x$
$\bullet$ Power of the variable $x$ is $2$

Let's take a look at each option separately.
$\bullet$ (a.) $\underset{–}{3x:}$
The power of the variable $x$ is $1$ but in $9x^2$, the power of variable $x$ is $2$. So, $3x$ and $9x^2$ are not like terms.

$\bullet$ (b.) $\underset{–}{81x^2:}$
The power of the variable $x$ is $2$ and also in $9x^2$, the power of variable $x$ is $2$. So, $81x^2$ and $9x^2$ are like terms.

$\bullet$ (c.) $\underset{–}{99x^2:}$
The power of the variable $x$ is $2$ and also in $9x^2$, the power of variable $x$ is $2$. So, $99x^2$ and $9x^2$ are like terms.

$\bullet$ (d.) $\underset{–}{729x^3:}$
The power of the variable $x$ is $3$ but in $9x^2$, the power of variable $x$ is $2$. So, $729x^3$ and $9x^2$ are not like terms.

Hence, option(a.) and option (d.) are correct.