Question

Which of the following is a like term of 7xy?(A) 8xy2 (B)-8xy(C) 16 x2 y 2 (D) 7 x2 y​

Answer 1

We need to recall the definition of like terms.

Terms whose variables (such as x or y) with any exponents (such as the 2 in x2) are the same.

Like terms are terms which have same variables with exponents.

Given:

The term is $7xy$

$8xy^{2},16 x^{2} y^{2} ,7.2y$ can't be the like terms as they don't have same variables and exponents

$-8xy$ is the like term of $7xy$

Hence, option (B) is correct

Answer 2

The like term of 7xy is -8xy (option B).

• The like terms are terms with the same number of variables but different or the same coefficients. If they have x and y as variables then their power should be the same. The power of x will be compared with x and the power of y will be compared with y.
• Option (A) $8xy^2$ has y with power 2 but 7xy has y with power 1.  So, this option is also incorrect.

• Option (B) $-8xy$ has x and y with power 1 each and 7xy has also x and y with power 1 each. So they are like terms.

• Option (C) $16x^2y^2$ has both x and y with power 2 but 7xy has x and y with power 1. So, this option is also incorrect.
• Option (D) $7x^2y$ has both x and y with power 2 and 1 respectively but 7xy has x and y with power 1. So, this option is also incorrect.