To determine which set contains like terms, we need to understand that like terms are terms that have the same variable part (including the same exponent). Constants without variables can also be considered like terms among themselves. Let's analyze each option step-by-step:
### Option (a) [tex]\(\{19y, 19, y\}\)[/tex]
- 19y: This term has the variable [tex]\( y \)[/tex].
- 19: This is a constant, with no variable.
- y: This term has the variable [tex]\( y \)[/tex].
Here, [tex]\(19y\)[/tex] and [tex]\(y\)[/tex] have the same variable part [tex]\(y\)[/tex], but [tex]\(19\)[/tex] does not have any variable. Therefore, this set does not consist entirely of like terms.
### Option (b) [tex]\(\{18x, -x, 21x\}\)[/tex]
- 18x: This term has the variable [tex]\( x \)[/tex].
- -x: This term also has the variable [tex]\( x \)[/tex].
- 21x: This term also has the variable [tex]\( x \)[/tex].
All these terms ([tex]\( 18x \)[/tex], [tex]\( -x \)[/tex], and [tex]\( 21x \)[/tex]) have the same variable part [tex]\( x \)[/tex]. Thus, they are all like terms.
### Option (c) [tex]\(\{15, 20, 25y\}\)[/tex]
- 15: This is a constant, with no variable.
- 20: This is also a constant, with no variable.
- 25y: This term has the variable [tex]\( y \)[/tex].
Here, [tex]\(15\)[/tex] and [tex]\(20\)[/tex] are like terms as they are both constants. However, [tex]\(25y\)[/tex] has a variable [tex]\( y \)[/tex], making it different from the constants. Therefore, this set does not consist entirely of like terms.
### Option (d) [tex]\(\{-2x, -2y, -2xy\}\)[/tex]
- -2x: This term has the variable [tex]\( x \)[/tex].
- -2y: This term has the variable [tex]\( y \)[/tex].
- -2xy: This term has the variable part [tex]\( xy \)[/tex].
The terms [tex]\( -2x \)[/tex], [tex]\( -2y \)[/tex], and [tex]\( -2xy \)[/tex] all have different variable parts ([tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( xy \)[/tex]), respectively. Thus, they are not like terms.
### Conclusion
From the analysis above, the set of like terms is:
(b) [tex]\(\{18x, -x, 21x\}\)[/tex]
