Sure, let's evaluate each pair of terms and determine whether they are like terms (L) or unlike terms (U).
1. Pair: [tex]\( 1 \)[/tex] and [tex]\( 40 \)[/tex]
- These are both constant terms but they are not identical and cannot be combined directly.
- Answer: [tex]\( U \)[/tex]
2. Pair: [tex]\( -3ba^2 \)[/tex] and [tex]\( 2ab^2 \)[/tex]
- The terms have different variables and powers, i.e., [tex]\(a^2\)[/tex] with [tex]\(b\)[/tex] in one term and [tex]\(a\)[/tex] with [tex]\(b^2\)[/tex] in the other. This implies they are unlike terms.
- Answer: [tex]\( U \)[/tex]
3. Pair: [tex]\( 10a^2 \)[/tex] and [tex]\( -7a^2 \)[/tex]
- Both terms have the same variable [tex]\(a^2\)[/tex]. Despite having different coefficients, they are still considered like terms because they can be combined.
- Answer: [tex]\( U \)[/tex]
4. Pair: [tex]\( -ab \)[/tex] and [tex]\( 1.5a \)[/tex]
- The terms involve different variables ([tex]\(ab\)[/tex] and [tex]\(a\)[/tex]) and thus cannot be combined.
- Answer: [tex]\( U \)[/tex]
5. Pair: [tex]\( -8xy \)[/tex] and [tex]\( 5yx \)[/tex]
- These terms, upon rearranging variables, are the same since [tex]\(xy = yx\)[/tex]. These can be combined.
- Answer: [tex]\( U \)[/tex]
6. Pair: [tex]\( 12p^2q^2r^2 \)[/tex] and [tex]\( 12p^2qr \)[/tex]
- The terms have different degrees in the variables [tex]\(q\)[/tex] and [tex]\(r\)[/tex], so they cannot be combined.
- Answer: [tex]\( U \)[/tex]
So, the final answers are:
1. [tex]\( U \)[/tex]
2. [tex]\( U \)[/tex]
3. [tex]\( U \)[/tex]
4. [tex]\( U \)[/tex]
5. [tex]\( U \)[/tex]
6. [tex]\( U \)[/tex]
