Question

Which of the following are like terms?
A) $11xy{z^2}, - 18x{y^2}z$
B) $7xy{z^2}, - 7xy{z^2}$
C) $17xy{z^2},7{x^2}yz$
D) $3{x^2}{y^2}{z^2},13xy{z^2}$

Answer 1

Hint: Two terms are like if the variables and its exponents are the same. It is not necessary that the coefficients are the same. So using this idea we can find the like terms.

Complete step-by-step answer:
There are four options. We have to find which of the pair contains two like terms.
We know that the terms having the same variable with same exponents are called like terms. Coefficients can be different.
A) $11xy{z^2}, - 18x{y^2}z$
In this option, the variables are the same. But the exponents are different.
$y$ has exponent one in first term but exponent two in second term.
So the terms are not like.
B) $7xy{z^2}, - 7xy{z^2}$
In this option, the variables are the same. Also the exponents are the same.
So the terms are like.
C) $17xy{z^2},7{x^2}yz$
In this option, the variables are the same. But the exponents are different.
$z$ has exponent two in first term but exponent one in second term.
So the terms are not like.
D) $3{x^2}{y^2}{z^2},13xy{z^2}$
In this option, the variables are the same. But the exponents are different.
$x$ has exponent two in first term but exponent one in second term.
So the terms are not like.

$\therefore $ The correct answer is option B.

Note: Be careful about the definition while finding like terms. Variables and their exponents must be the same. Coefficients can be different. So if two terms are like, one term will be a constant multiple of the other. Otherwise the terms are said to be unlike.