Students can cut out these algebraic expressions to practice simplifying and grouping equivalent terms.

- 4x + 2y + 8 → 2(2x + y + 4)
- (8x + 3y - 15) - (3y + 13) → 8x - 28
- (4x + 9y + 13) - (4x - 5) → 9y + 18
- 2(2x + y + 4) → 4x + 2y + 8
- 8x - 28 → (8x + 3y - 15) - (3y + 13)
- 4x + 16y + 20 → 4(2x - 7) is incorrect; correct pair: 4x + 16y + 20 → (2x + y - 6) + (4x - 3y + 10) is incorrect; re-evaluate: 4x + 16y + 20 = 4(x + 4y + 5), no direct match in list. Wait, let's recalculate all.

Correct groupings after simplifying each expression:

Group 1: 4x + 2y + 8 and 2(2x + y + 4) → both simplify to 4x + 2y + 8

Group 2: (8x + 3y - 15) - (3y + 13) = 8x - 28 and 8x - 28 → both are 8x - 28

Group 3: (4x + 9y + 13) - (4x - 5) = 9y + 18 and 9y + 18 → both are 9y + 18

Group 4: 4x + 16y + 20 and (2x + y - 6) + (4x - 3y + 10) = 6x - 2y + 4 — not equal. Let’s simplify (2x + y - 6) + (4x - 3y + 10) = 6x - 2y + 4. So 4x + 16y + 20 does not match this.

Wait, let’s simplify every expression:

1. 4x + 2y + 8 → already simplified
2. 6x + 9y - 15 → already simplified
3. (8x + 3y - 15) - (3y + 13) = 8x + 3y - 15 - 3y - 13 = 8x - 28
4. 3(2x + 3y - 5) = 6x + 9y - 15
5. (4x + 9y + 13) - (4x - 5) = 4x + 9y + 13 - 4x + 5 = 9y + 18
6. 2(3x - y + 2) = 6x - 2y + 4
7. 2(2x + y + 4) = 4x + 2y + 8
8. (x + 16y + 11) + (3x + 9) = 4x + 16y + 20
9. (2x + y - 6) + (4x - 3y + 10) = 6x - 2y + 4
10. 8x - 28 → already simplified
11. 4x + 16y + 20 → already simplified
12. (9x + 19y + 20) - (5x + 3y) = 4x + 16y + 20
13. 9y + 18 → already simplified
14. (9x + 11y - 10) - (3x + 2y + 5) = 6x + 9y - 15
15. (11x + 3y + 8) - (7x + y) = 4x + 2y + 8
16. 6x - 2y + 4 → already simplified
17. 4(2x - 7) = 8x - 28
18. (-y - 3) + (10y + 21) = 9y + 18

Now group by simplified form:

Group A (4x + 2y + 8):
- 4x + 2y + 8
- 2(2x + y + 4)
- (11x + 3y + 8) - (7x + y)

Group B (6x + 9y - 15):
- 6x + 9y - 15
- 3(2x + 3y - 5)
- (9x + 11y - 10) - (3x + 2y + 5)

Group C (8x - 28):
- (8x + 3y - 15) - (3y + 13)
- 8x - 28
- 4(2x - 7)

Group D (9y + 18):
- (4x + 9y + 13) - (4x - 5)
- 9y + 18
- (-y - 3) + (10y + 21)

Group E (6x - 2y + 4):
- 2(3x - y + 2)
- (2x + y - 6) + (4x - 3y + 10)

Group F (4x + 16y + 20):
- (x + 16y + 11) + (3x + 9)
- (9x + 19y + 20) - (5x + 3y)

Final grouped list:

- 4x + 2y + 8, 2(2x + y + 4), (11x + 3y + 8) - (7x + y)
- 6x + 9y - 15, 3(2x + 3y - 5), (9x + 11y - 10) - (3x + 2y + 5)
- (8x + 3y - 15) - (3y + 13), 8x - 28, 4(2x - 7)
- (4x + 9y + 13) - (4x - 5), 9y + 18, (-y - 3) + (10y + 21)
- 2(3x - y + 2), (2x + y - 6) + (4x - 3y + 10)
- (x + 16y + 11) + (3x + 9), (9x + 19y + 20) - (5x + 3y)