Question

Which of the following is a pair of like terms?

• A. $–7x{y}^{2}z,–7x^{2}yz$
• B. $–10xy{z}^2,3xy{z}^2$
• C. $3xyz,3x^2{y}^2{z}^2$
• D. $4xy{z}^2,4x^{2}yz$

Answer 1

The correct option is B

$–10xy{z}^2,3xy{z}^2$

Explanation for correct answers:

Determine the pair of like terms:

Like terms are the terms that exactly have the same variables with equal powers.

The terms $–10xy{z}^2,3xy{z}^2$ have the same variables with the same powers.

So, $–10xy{z}^2,3xy{z}^2$ are like terms.

Thus, option B is correct.

Explanation for all incorrect answers:

The exponent of $x$ in the term $–7x{y}^{2}z$ is $1$ but $2$ in $–7x^{2}yz$.

So, $–7x{y}^{2}z,–7x^{2}yz$ are not like terms.

Thus, option A is incorrect.

The exponent of $x$ in the term $3xyz$ is $1$ but $2$ in $3x^2{y}^2{z}^2$.

So, $3xyz,3x^2{y}^2{z}^2$ are not like terms.

Thus, option C is incorrect.

The exponent of $x$ in the term $4xy{z}^2$ is $1$ but $2$ in $4x^{2}yz$.

So, $4xy{z}^2,4x^{2}yz$ are not like terms.

Thus, option D is incorrect.

Hence, the correct option is 'B'.