Question

Match the following terms with like terms:
−4g^4 -4g^3 2g^3 -18g^3v -18gv^3 2v^3 48g^3v 48gv^3 -4v^3 2g^4

Answer 1

To match the given terms with like terms, we need to identify which terms have the same variable(s) raised to the same power.

Here are the terms you provided:

1. \(-4g^4\)
2. \(-4g^3\)
3. \(2g^3\)
4. \(-18g^3v\)
5. \(-18gv^3\)
6. \(2v^3\)
7. \(48g^3v\)
8. \(48gv^3\)
9. \(-4v^3\)
10. \(2g^4\)

Now let's group the like terms:

- **Terms with \(g^4\):**
- \(-4g^4\)
- \(2g^4\)

- **Terms with \(g^3\):**
- \(-4g^3\)
- \(2g^3\)
- \(-18g^3v\)
- \(48g^3v\)

- **Terms with \(gv^3\):**
- \(-18gv^3\)
- \(48gv^3\)

- **Terms with \(v^3\):**
- \(2v^3\)
- \(-4v^3\)

Here they are matched accordingly:

1. \(-4g^4\) ➔ \(2g^4\)
2. \(-4g^3\) ➔ \(2g^3\)
3. \(-18g^3v\) ➔ \(48g^3v\)
4. \(-18gv^3\) ➔ \(48gv^3\)
5. \(2v^3\) ➔ \(-4v^3\)

Each of these terms is matched with others that share the same powers of their respective variables. Let me know if you need further assistance!