Which of the following are like terms? (a) $5 x y z^{2}, - 3 x y^{2} z$ (b) $- 5 x y z^{2}, 7 x y z^{2}$ (c) $5 x y z^{2}, 5 x^{2} y z$ (d) $5 x y z^{2}, x^{2} y^{2} z^{2}$

option (b) is correct.

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options (a), (c), and (d) are incorrect.

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Solution

The correct option is A
option (b) is correct.

Explanation for the correct option:
Option (b): Determine the like terms.
The same variables are used to create like terms, and their powers are also the same and the coefficients of like terms do not require to be the same.
$- 5 x y z^{2}, 7 x y z^{2}$ is like terms since $- 5 x y z^{2}, 7 x y z^{2}$ have the same variables with the same powers.
Hence, option (b) is correct.
Explanation for the incorrect options:
Options (a): The expressions $5 x y z^{2}, - 3 x y^{2} z$ have the same variable but have different powers. So, $5 x y z^{2}, - 3 x y^{2} z$ is not like term.
Options (c): The expressions $5 x y z^{2}, 5 x^{2} y z$ have the same variable but have different powers. So, $5 x y z^{2}, 5 x^{2} y z$ is not like term.
Options (d): The expressions $5 x y z^{2}, x^{2} y^{2} z^{2}$ have the same variable but have different powers. So, $5 x y z^{2}, x^{2} y^{2} z^{2}$ is not like term.
Therefore, options (a), (c), and (d) are incorrect.
Hence, option (b) is correct.

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