Let's match each expression from list a-e to the corresponding expression in list 1-5 based on their similar terms:
1. Find the match for [tex]\(4xy^3\)[/tex]:
- This expression contains the terms [tex]\(x\)[/tex] and [tex]\(y^3\)[/tex].
- Looking through the second list, the expression that similarly includes [tex]\(x\)[/tex] and [tex]\(y^3\)[/tex] is [tex]\(8xy^3\)[/tex].
- Therefore, [tex]\(4xy^3\)[/tex] matches with [tex]\(8xy^3\)[/tex].
2. Find the match for [tex]\(14xy\)[/tex]:
- This expression contains the terms [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
- In the second list, the expression that similarly contains [tex]\(x\)[/tex] and [tex]\(y\)[/tex] is [tex]\(6xy\)[/tex].
- Therefore, [tex]\(14xy\)[/tex] matches with [tex]\(6xy\)[/tex].
3. Find the match for [tex]\(15y^2\)[/tex]:
- This expression contains the term [tex]\(y^2\)[/tex].
- In the second list, the expression that contains [tex]\(y^2\)[/tex] is [tex]\(-3y^2\)[/tex].
- Therefore, [tex]\(15y^2\)[/tex] matches with [tex]\(-3y^2\)[/tex].
4. Find the match for [tex]\(-6\)[/tex]:
- This expression is a constant (no variables).
- In the second list, the expression that is a constant is [tex]\(11\)[/tex].
- Therefore, [tex]\(-6\)[/tex] matches with [tex]\(11\)[/tex].
5. Find the match for [tex]\(5x^2\)[/tex]:
- This expression contains the term [tex]\(x^2\)[/tex].
- In the second list, the expression that contains [tex]\(x^2\)[/tex] is [tex]\(-12x^2\)[/tex].
- Therefore, [tex]\(5x^2\)[/tex] matches with [tex]\(-12x^2\)[/tex].
In summary, the matches are:
- [tex]\(4xy^3\)[/tex] matches with [tex]\(8xy^3\)[/tex].
- [tex]\(14xy\)[/tex] matches with [tex]\(6xy\)[/tex].
- [tex]\(15y^2\)[/tex] matches with [tex]\(-3y^2\)[/tex].
- [tex]\(-6\)[/tex] matches with [tex]\(11\)[/tex].
- [tex]\(5x^2\)[/tex] matches with [tex]\(-12x^2\)[/tex].
Putting it all together, we get the following matched pairs:
- [tex]\(a\)[/tex]: [tex]\(4xy^3\)[/tex] matches with [tex]\(4\)[/tex] (which is [tex]\(8xy^3\)[/tex])
- [tex]\(b\)[/tex]: [tex]\(14xy\)[/tex] matches with [tex]\(2\)[/tex] (which is [tex]\(6xy\)[/tex])
- [tex]\(c\)[/tex]: [tex]\(15y^2\)[/tex] matches with [tex]\(5\)[/tex] (which is [tex]\(-3y^2\)[/tex])
- [tex]\(d\)[/tex]: [tex]\(-6\)[/tex] matches with [tex]\(3\)[/tex] (which is [tex]\(11\)[/tex])
- [tex]\(e\)[/tex]: [tex]\(5x^2\)[/tex] matches with [tex]\(1\)[/tex] (which is [tex]\(-12x^2\)[/tex])
Thus, the final matched pairs are:
[tex]\[
\{ a: 4, b: 2, c: 5, d: 3, e: 1 \}
\][/tex]
