Question

what are like terms

Answer 1

"Like terms" are terms in an algebraic expression that have the exact same variable part (same variables raised to the same powers). Only the numerical coefficients can be different.

Key points
- Variables and their exponents must match exactly. Example: 3x^2 and -5x^2 are like terms.
- The order of variables doesn't matter: xy and yx are like terms.
- Constants (numbers with no variable) are like terms with other constants: 4 and -7 are like terms.
- Terms with different variables or different powers are not like terms: 2x and 2x^2 are not like terms; 3xy and 3x^2y are not like terms.

How to combine like terms
- Add or subtract only like terms by adding/subtracting their coefficients and keeping the common variable part.
Example: 3x + 5x = (3+5)x = 8x
Example: 4x^2 − 7x^2 = −3x^2
Example: 6 − 2 = 4

Examples
- Like terms: 2a and −7a; 5xy and 0.5yx; 3 and −1
- Not like terms: x and x^2; 4x and 4y; 2x^2y and 2xy^2

Quick practice (answers below)
1) Combine: 5x + 2x
2) Combine: 7ab − 3ba + 2ab
3) Are 3x^2 and −x^2 like terms?
4) Combine: 6 − 2 + 3

Answers
1) 7x
2) 6ab (because ab, ba same)
3) Yes — both are x^2 terms, so 3x^2 + (−x^2) = 2x^2
4) 7

If you want, I can give more examples or practice problems at your level.