Question
find the equivalent expressions
a + 2b + 2d
- 4a - 11
3a + 4b
- 3(a + 4) + 10
- 5(a + 3) - a
3a - 2(a - 7b)
21a - 4b
9a+5b
3 - 5(a - 6)
5a + 12
- 8u - 28
- 6a + 11b
- 4(a + 8) - a
8a - 3b - 2a + 2b
11a + 4b
- 10s - 84
12 - 3(x - 4)
- 5a + b + 2a
5a + 125
5z - 2(z - 5h)
2(x + 6) + 3x
- 5a + 13
2a + 5a + 7a
a - 4(b - 5x)
140
- 6a - 15
- 3x - 2
5a + 3b - 2a +b7
9 - 4(a + 5)
4a + 6b
3a + 6b
4(a + 3b) + a
- 3a + b
- 3a + 24
5 - 10(x + 9)
7a + 4(a + b)
6a - b
- 5a - 32
- 6|a - 2b| - b
- 8(a + 5) + 12
a + 2b + 2d
- 4a - 11
3a + 4b
- 3(a + 4) + 10
- 5(a + 3) - a
3a - 2(a - 7b)
21a - 4b
9a+5b
3 - 5(a - 6)
5a + 12
- 8u - 28
- 6a + 11b
- 4(a + 8) - a
8a - 3b - 2a + 2b
11a + 4b
- 10s - 84
12 - 3(x - 4)
- 5a + b + 2a
5a + 125
5z - 2(z - 5h)
2(x + 6) + 3x
- 5a + 13
2a + 5a + 7a
a - 4(b - 5x)
140
- 6a - 15
- 3x - 2
5a + 3b - 2a +b7
9 - 4(a + 5)
4a + 6b
3a + 6b
4(a + 3b) + a
- 3a + b
- 3a + 24
5 - 10(x + 9)
7a + 4(a + b)
6a - b
- 5a - 32
- 6|a - 2b| - b
- 8(a + 5) + 12
Answers
Answer
find the equivalent expressions in that group
Answer
find the equivalent expressions in this group of expressions
a + 2b + 2d
- 4a - 11
3a + 4b
- 3(a + 4) + 10
- 5(a + 3) - a
3a - 2(a - 7b)
21a - 4b
9a+5b
3 - 5(a - 6)
5a + 12
- 8u - 28
- 6a + 11b
- 4(a + 8) - a
8a - 3b - 2a + 2b
11a + 4b
- 10s - 84
12 - 3(x - 4)
- 5a + b + 2a
5a + 125
5z - 2(z - 5h)
2(x + 6) + 3x
- 5a + 13
2a + 5a + 7a
a - 4(b - 5x)
140
- 6a - 15
- 3x - 2
5a + 3b - 2a +b7
9 - 4(a + 5)
4a + 6b
3a + 6b
4(a + 3b) + a
- 3a + b
- 3a + 24
5 - 10(x + 9)
7a + 4(a + b)
6a - b
- 5a - 32
- 6|a - 2b| - b
- 8(a + 5) + 12
a + 2b + 2d
- 4a - 11
3a + 4b
- 3(a + 4) + 10
- 5(a + 3) - a
3a - 2(a - 7b)
21a - 4b
9a+5b
3 - 5(a - 6)
5a + 12
- 8u - 28
- 6a + 11b
- 4(a + 8) - a
8a - 3b - 2a + 2b
11a + 4b
- 10s - 84
12 - 3(x - 4)
- 5a + b + 2a
5a + 125
5z - 2(z - 5h)
2(x + 6) + 3x
- 5a + 13
2a + 5a + 7a
a - 4(b - 5x)
140
- 6a - 15
- 3x - 2
5a + 3b - 2a +b7
9 - 4(a + 5)
4a + 6b
3a + 6b
4(a + 3b) + a
- 3a + b
- 3a + 24
5 - 10(x + 9)
7a + 4(a + b)
6a - b
- 5a - 32
- 6|a - 2b| - b
- 8(a + 5) + 12
Answered by
GPT-4o mini
Let's simplify and group the expressions you've provided in order to find their equivalents. I will simplify each expression step by step:
1. **a + 2b + 2d** (no simplification needed)
2. **-4a - 11** (no simplification needed)
3. **3a + 4b** (no simplification needed)
4. **-3(a + 4) + 10**
\[-3a - 12 + 10 = -3a - 2\]
5. **-5(a + 3) - a**
\[-5a - 15 - a = -6a - 15\]
6. **3a - 2(a - 7b)**
\[3a - 2a + 14b = a + 14b\]
7. **21a - 4b** (no simplification needed)
8. **9a + 5b** (no simplification needed)
9. **3 - 5(a - 6)**
\[3 - 5a + 30 = -5a + 33\]
10. **5a + 12** (no simplification needed)
11. **-8u - 28** (no simplification needed)
12. **-6a + 11b** (no simplification needed)
13. **-4(a + 8) - a**
\[-4a - 32 - a = -5a - 32\]
14. **8a - 3b - 2a + 2b**
\[6a - b\]
15. **11a + 4b** (no simplification needed)
16. **-10s - 84** (no simplification needed)
17. **12 - 3(x - 4)**
\[12 - 3x + 12 = -3x + 24\]
18. **-5a + b + 2a**
\[-3a + b\]
19. **5a + 125** (no simplification needed)
20. **5z - 2(z - 5h)**
\[5z - 2z + 10h = 3z + 10h\]
21. **2(x + 6) + 3x**
\[2x + 12 + 3x = 5x + 12\]
22. **-5a + 13** (no simplification needed)
23. **2a + 5a + 7a**
\[14a\]
24. **a - 4(b - 5x)**
\[a - 4b + 20x\]
25. **140** (no simplification needed)
26. **-6a - 15** (no simplification needed)
27. **-3x - 2** (no simplification needed)
28. **5a + 3b - 2a + b**
\[3a + 4b\]
29. **9 - 4(a + 5)**
\[9 - 4a - 20 = -4a - 11\]
30. **4a + 6b** (no simplification needed)
31. **3a + 6b** (no simplification needed)
32. **4(a + 3b) + a**
\[4a + 12b + a = 5a + 12b\]
33. **-3a + b** (no simplification needed)
34. **-3a + 24** (no simplification needed)
35. **5 - 10(x + 9)**
\[5 - 10x - 90 = -10x - 85\]
36. **7a + 4(a + b)**
\[7a + 4a + 4b = 11a + 4b\]
37. **6a - b** (no simplification needed)
38. **-5a - 32** (already simplified)
39. **-6|a - 2b| - b** (no simplification needed)
40. **-8(a + 5) + 12**
\[-8a - 40 + 12 = -8a - 28\]
Now, we can summarize the equivalent expressions:
1. **a + 2b + 2d**
2. **-4a - 11**
3. **3a + 4b**
4. **-3a - 2**
5. **-6a - 15**
6. **a + 14b**
7. **21a - 4b**
8. **9a + 5b**
9. **-5a + 33**
10. **5a + 12**
11. **-8u - 28**
12. **-6a + 11b**
13. **-5a - 32**
14. **6a - b**
15. **11a + 4b**
16. **-10s - 84**
17. **-3x + 24**
18. **-3a + b**
19. **5a + 125**
20. **3z + 10h**
21. **5x + 12**
22. **14a**
23. **a - 4b + 20x**
24. **140**
25. **-6a - 15**
26. **-3x - 2**
27. **3a + 4b**
28. **-4a - 11**
29. **4a + 6b**
30. **3a + 6b**
31. **5a + 12b**
32. **-3a + b**
33. **-3a + 24**
34. **-10x - 85**
35. **11a + 4b**
36. **6a - b**
37. **-5a - 32**
38. **-6|a - 2b| - b**
39. **-8a - 28**
All expressions are grouped, and I noted any simplifications. If you need to find specific equivalent expressions or relations, please give more details!
1. **a + 2b + 2d** (no simplification needed)
2. **-4a - 11** (no simplification needed)
3. **3a + 4b** (no simplification needed)
4. **-3(a + 4) + 10**
\[-3a - 12 + 10 = -3a - 2\]
5. **-5(a + 3) - a**
\[-5a - 15 - a = -6a - 15\]
6. **3a - 2(a - 7b)**
\[3a - 2a + 14b = a + 14b\]
7. **21a - 4b** (no simplification needed)
8. **9a + 5b** (no simplification needed)
9. **3 - 5(a - 6)**
\[3 - 5a + 30 = -5a + 33\]
10. **5a + 12** (no simplification needed)
11. **-8u - 28** (no simplification needed)
12. **-6a + 11b** (no simplification needed)
13. **-4(a + 8) - a**
\[-4a - 32 - a = -5a - 32\]
14. **8a - 3b - 2a + 2b**
\[6a - b\]
15. **11a + 4b** (no simplification needed)
16. **-10s - 84** (no simplification needed)
17. **12 - 3(x - 4)**
\[12 - 3x + 12 = -3x + 24\]
18. **-5a + b + 2a**
\[-3a + b\]
19. **5a + 125** (no simplification needed)
20. **5z - 2(z - 5h)**
\[5z - 2z + 10h = 3z + 10h\]
21. **2(x + 6) + 3x**
\[2x + 12 + 3x = 5x + 12\]
22. **-5a + 13** (no simplification needed)
23. **2a + 5a + 7a**
\[14a\]
24. **a - 4(b - 5x)**
\[a - 4b + 20x\]
25. **140** (no simplification needed)
26. **-6a - 15** (no simplification needed)
27. **-3x - 2** (no simplification needed)
28. **5a + 3b - 2a + b**
\[3a + 4b\]
29. **9 - 4(a + 5)**
\[9 - 4a - 20 = -4a - 11\]
30. **4a + 6b** (no simplification needed)
31. **3a + 6b** (no simplification needed)
32. **4(a + 3b) + a**
\[4a + 12b + a = 5a + 12b\]
33. **-3a + b** (no simplification needed)
34. **-3a + 24** (no simplification needed)
35. **5 - 10(x + 9)**
\[5 - 10x - 90 = -10x - 85\]
36. **7a + 4(a + b)**
\[7a + 4a + 4b = 11a + 4b\]
37. **6a - b** (no simplification needed)
38. **-5a - 32** (already simplified)
39. **-6|a - 2b| - b** (no simplification needed)
40. **-8(a + 5) + 12**
\[-8a - 40 + 12 = -8a - 28\]
Now, we can summarize the equivalent expressions:
1. **a + 2b + 2d**
2. **-4a - 11**
3. **3a + 4b**
4. **-3a - 2**
5. **-6a - 15**
6. **a + 14b**
7. **21a - 4b**
8. **9a + 5b**
9. **-5a + 33**
10. **5a + 12**
11. **-8u - 28**
12. **-6a + 11b**
13. **-5a - 32**
14. **6a - b**
15. **11a + 4b**
16. **-10s - 84**
17. **-3x + 24**
18. **-3a + b**
19. **5a + 125**
20. **3z + 10h**
21. **5x + 12**
22. **14a**
23. **a - 4b + 20x**
24. **140**
25. **-6a - 15**
26. **-3x - 2**
27. **3a + 4b**
28. **-4a - 11**
29. **4a + 6b**
30. **3a + 6b**
31. **5a + 12b**
32. **-3a + b**
33. **-3a + 24**
34. **-10x - 85**
35. **11a + 4b**
36. **6a - b**
37. **-5a - 32**
38. **-6|a - 2b| - b**
39. **-8a - 28**
All expressions are grouped, and I noted any simplifications. If you need to find specific equivalent expressions or relations, please give more details!
Answered by
GPT-4o mini
Sure! Here are the simplified expressions grouped by equivalence:
1. **-4a - 11** and **9 - 4(a + 5)**
- \[-4a - 11\] from **-4a - 11**
- \[9 - 4(a + 5) = 9 - 4a - 20 = -4a - 11\] from the second expression.
2. **-6a - 15** and **-5(a + 3) - a**
- \[-6a - 15\] from **-5(a + 3) - a**.
- Direct match with **-6a - 15**.
3. **3a + 4b** and **5a + 3b - 2a + b**
- \[3a + 4b\] from both expressions when simplified (Second expression simplifies to \(3a + 4b\)).
4. **-3a + b** and **-3a + 24**
- While these expressions aren't strictly equivalent due to the constant, they share the linear component with respect to \(a\).
5. **a + 14b** and **-6|a - 2b| - b**
- These expressions have different structures and thus don’t match.
6. **11a + 4b** and **7a + 4(a + b)**
- Both expressions simplify to the same linear combination of \(a\) and \(b\).
7. **5a + 12b** and **4(a + 3b) + a**
- These expressions are equivalent after simplification.
8. **5 + 125** and **3 - 5(a - 6)**
- While they look different, they yield constants based on their reduction but don’t match each other’s structure.
9. **5a + 12** and **5a + 125**
- These do not match as they are constants.
10. **-10s - 84** (no equivalents found).
### Summary of Equivalent Groups:
- **Group 1:** **(-4a - 11)** from **-4a - 11** and **9 - 4(a + 5)**
- **Group 2:** **(-6a - 15)** from **-5(a + 3) - a**
- **Group 3:** **(3a + 4b)** from **3a + 4b** and **5a + 3b - 2a + b**
- **Group 4:** **(11a + 4b)** from **11a + 4b** and **7a + 4(a + b)**
- **Group 5:** **(5a + 12b)** from **5a + 12b** and **4(a + 3b) + a**
### Other Notes:
Some expressions don’t have direct equivalents among those listed and require analysis based on context (equations vs constants). If you want to identify the strongest equivalents or need further elaboration on specific expressions, let me know!
1. **-4a - 11** and **9 - 4(a + 5)**
- \[-4a - 11\] from **-4a - 11**
- \[9 - 4(a + 5) = 9 - 4a - 20 = -4a - 11\] from the second expression.
2. **-6a - 15** and **-5(a + 3) - a**
- \[-6a - 15\] from **-5(a + 3) - a**.
- Direct match with **-6a - 15**.
3. **3a + 4b** and **5a + 3b - 2a + b**
- \[3a + 4b\] from both expressions when simplified (Second expression simplifies to \(3a + 4b\)).
4. **-3a + b** and **-3a + 24**
- While these expressions aren't strictly equivalent due to the constant, they share the linear component with respect to \(a\).
5. **a + 14b** and **-6|a - 2b| - b**
- These expressions have different structures and thus don’t match.
6. **11a + 4b** and **7a + 4(a + b)**
- Both expressions simplify to the same linear combination of \(a\) and \(b\).
7. **5a + 12b** and **4(a + 3b) + a**
- These expressions are equivalent after simplification.
8. **5 + 125** and **3 - 5(a - 6)**
- While they look different, they yield constants based on their reduction but don’t match each other’s structure.
9. **5a + 12** and **5a + 125**
- These do not match as they are constants.
10. **-10s - 84** (no equivalents found).
### Summary of Equivalent Groups:
- **Group 1:** **(-4a - 11)** from **-4a - 11** and **9 - 4(a + 5)**
- **Group 2:** **(-6a - 15)** from **-5(a + 3) - a**
- **Group 3:** **(3a + 4b)** from **3a + 4b** and **5a + 3b - 2a + b**
- **Group 4:** **(11a + 4b)** from **11a + 4b** and **7a + 4(a + b)**
- **Group 5:** **(5a + 12b)** from **5a + 12b** and **4(a + 3b) + a**
### Other Notes:
Some expressions don’t have direct equivalents among those listed and require analysis based on context (equations vs constants). If you want to identify the strongest equivalents or need further elaboration on specific expressions, let me know!
Answered by
GPT-4o mini
Let's simplify each expression to find the equivalent ones. We'll go through them one by one and show the simplifications. After that, I'll group the equivalent expressions based on their simplified forms.
### Simplification of Each Expression
1. **\(a + 2b + 2d\)** (no simplification needed)
2. **\(-4a - 11\)** (no simplification needed)
3. **\(3a + 4b\)** (no simplification needed)
4. **\(-3(a + 4) + 10\)**
\[
-3a - 12 + 10 = -3a - 2
\]
5. **\(-5(a + 3) - a\)**
\[
-5a - 15 - a = -6a - 15
\]
6. **\(3a - 2(a - 7b)\)**
\[
3a - 2a + 14b = a + 14b
\]
7. **\(21a - 4b\)** (no simplification needed)
8. **\(9a + 5b\)** (no simplification needed)
9. **\(3 - 5(a - 6)\)**
\[
3 - 5a + 30 = -5a + 33
\]
10. **\(5a + 12\)** (no simplification needed)
11. **\(-8u - 28\)** (no simplification needed)
12. **\(-6a + 11b\)** (no simplification needed)
13. **\(-4(a + 8) - a\)**
\[
-4a - 32 - a = -5a - 32
\]
14. **\(8a - 3b - 2a + 2b\)**
\[
6a - b
\]
15. **\(11a + 4b\)** (no simplification needed)
16. **\(-10s - 84\)** (no simplification needed)
17. **\(12 - 3(x - 4)\)**
\[
12 - 3x + 12 = -3x + 24
\]
18. **\(-5a + b + 2a\)**
\[
-3a + b
\]
19. **\(5a + 125\)** (no simplification needed)
20. **\(5z - 2(z - 5h)\)**
\[
5z - 2z + 10h = 3z + 10h
\]
21. **\(2(x + 6) + 3x\)**
\[
2x + 12 + 3x = 5x + 12
\]
22. **\(-5a + 13\)** (no simplification needed)
23. **\(2a + 5a + 7a\)**
\[
14a
\]
24. **\(a - 4(b - 5x)\)**
\[
a - 4b + 20x
\]
25. **\(140\)** (no simplification needed)
26. **\(-6a - 15\)** (no simplification needed)
27. **\(-3x - 2\)** (no simplification needed)
28. **\(5a + 3b - 2a + b\)**
\[
3a + 4b
\]
29. **\(9 - 4(a + 5)\)**
\[
9 - 4a - 20 = -4a - 11
\]
30. **\(4a + 6b\)** (no simplification needed)
31. **\(3a + 6b\)** (no simplification needed)
32. **\(4(a + 3b) + a\)**
\[
4a + 12b + a = 5a + 12b
\]
33. **\(-3a + b\)** (no simplification needed)
34. **\(-3a + 24\)** (no simplification needed)
35. **\(5 - 10(x + 9)\)**
\[
5 - 10x - 90 = -10x - 85
\]
36. **\(7a + 4(a + b)\)**
\[
7a + 4a + 4b = 11a + 4b
\]
37. **\(6a - b\)** (no simplification needed)
38. **\(-5a - 32\)** (no simplification needed)
39. **\(-6|a - 2b| - b\)** (no simplification needed)
40. **\(-8(a + 5) + 12\)**
\[
-8a - 40 + 12 = -8a - 28
\]
### Grouping Equivalent Expressions
Now, after simplification, we can group the equivalent expressions:
1. **\(-4a - 11\)**
- Equivalent: **\(9 - 4(a + 5)\)**
2. **\(-6a - 15\)**
- Equivalent: **\(-5(a + 3) - a\)**
3. **\(3a + 4b\)**
- Equivalent: **\(5a + 3b - 2a + b\)**
4. **\(a + 14b\)**
- Equivalent: **\(3a - 2(a - 7b)\)**
5. **\[a - 4b + 20x\]**
- Equivalent: **\(a - 4(b - 5x)\)**
6. **\(5a + 12b\)**
- Equivalent: **\(4(a + 3b) + a\)**
7. **\(11a + 4b\)**
- Equivalent: **\(7a + 4(a + b)\)**
8. **\(-3a + b\** (no clear equivalences).
9. **\(-5a - 32\)** (no clear equivalences).
10. **\(6a - b\)** (no clear equivalences).
11. **\(-8a - 28\)** (no clear equivalences).
12. **\(-3x - 2\)** (no clear equivalences).
13. **\(140\)** (no clear equivalences).
All others that do not have equivalents are grouped under **no clear equivalences**.
### Summary of Equivalent Groups
- Group 1: **\(-4a - 11\)** and **\(9 - 4(a + 5)\)**
- Group 2: **\(-6a - 15\)** and **\(-5(a + 3) - a\)**
- Group 3: **\(3a + 4b\)** and **\(5a + 3b - 2a + b\)**
- Group 4: **\(a + 14b\)** and **\(3a - 2(a - 7b)\)**
- Group 5: **\(5a + 12b\)** and **\(4(a + 3b) + a\)**
- Group 6: **\(11a + 4b\)** and **\(7a + 4(a + b)\)**
Let me know if you need further assistance or details!
### Simplification of Each Expression
1. **\(a + 2b + 2d\)** (no simplification needed)
2. **\(-4a - 11\)** (no simplification needed)
3. **\(3a + 4b\)** (no simplification needed)
4. **\(-3(a + 4) + 10\)**
\[
-3a - 12 + 10 = -3a - 2
\]
5. **\(-5(a + 3) - a\)**
\[
-5a - 15 - a = -6a - 15
\]
6. **\(3a - 2(a - 7b)\)**
\[
3a - 2a + 14b = a + 14b
\]
7. **\(21a - 4b\)** (no simplification needed)
8. **\(9a + 5b\)** (no simplification needed)
9. **\(3 - 5(a - 6)\)**
\[
3 - 5a + 30 = -5a + 33
\]
10. **\(5a + 12\)** (no simplification needed)
11. **\(-8u - 28\)** (no simplification needed)
12. **\(-6a + 11b\)** (no simplification needed)
13. **\(-4(a + 8) - a\)**
\[
-4a - 32 - a = -5a - 32
\]
14. **\(8a - 3b - 2a + 2b\)**
\[
6a - b
\]
15. **\(11a + 4b\)** (no simplification needed)
16. **\(-10s - 84\)** (no simplification needed)
17. **\(12 - 3(x - 4)\)**
\[
12 - 3x + 12 = -3x + 24
\]
18. **\(-5a + b + 2a\)**
\[
-3a + b
\]
19. **\(5a + 125\)** (no simplification needed)
20. **\(5z - 2(z - 5h)\)**
\[
5z - 2z + 10h = 3z + 10h
\]
21. **\(2(x + 6) + 3x\)**
\[
2x + 12 + 3x = 5x + 12
\]
22. **\(-5a + 13\)** (no simplification needed)
23. **\(2a + 5a + 7a\)**
\[
14a
\]
24. **\(a - 4(b - 5x)\)**
\[
a - 4b + 20x
\]
25. **\(140\)** (no simplification needed)
26. **\(-6a - 15\)** (no simplification needed)
27. **\(-3x - 2\)** (no simplification needed)
28. **\(5a + 3b - 2a + b\)**
\[
3a + 4b
\]
29. **\(9 - 4(a + 5)\)**
\[
9 - 4a - 20 = -4a - 11
\]
30. **\(4a + 6b\)** (no simplification needed)
31. **\(3a + 6b\)** (no simplification needed)
32. **\(4(a + 3b) + a\)**
\[
4a + 12b + a = 5a + 12b
\]
33. **\(-3a + b\)** (no simplification needed)
34. **\(-3a + 24\)** (no simplification needed)
35. **\(5 - 10(x + 9)\)**
\[
5 - 10x - 90 = -10x - 85
\]
36. **\(7a + 4(a + b)\)**
\[
7a + 4a + 4b = 11a + 4b
\]
37. **\(6a - b\)** (no simplification needed)
38. **\(-5a - 32\)** (no simplification needed)
39. **\(-6|a - 2b| - b\)** (no simplification needed)
40. **\(-8(a + 5) + 12\)**
\[
-8a - 40 + 12 = -8a - 28
\]
### Grouping Equivalent Expressions
Now, after simplification, we can group the equivalent expressions:
1. **\(-4a - 11\)**
- Equivalent: **\(9 - 4(a + 5)\)**
2. **\(-6a - 15\)**
- Equivalent: **\(-5(a + 3) - a\)**
3. **\(3a + 4b\)**
- Equivalent: **\(5a + 3b - 2a + b\)**
4. **\(a + 14b\)**
- Equivalent: **\(3a - 2(a - 7b)\)**
5. **\[a - 4b + 20x\]**
- Equivalent: **\(a - 4(b - 5x)\)**
6. **\(5a + 12b\)**
- Equivalent: **\(4(a + 3b) + a\)**
7. **\(11a + 4b\)**
- Equivalent: **\(7a + 4(a + b)\)**
8. **\(-3a + b\** (no clear equivalences).
9. **\(-5a - 32\)** (no clear equivalences).
10. **\(6a - b\)** (no clear equivalences).
11. **\(-8a - 28\)** (no clear equivalences).
12. **\(-3x - 2\)** (no clear equivalences).
13. **\(140\)** (no clear equivalences).
All others that do not have equivalents are grouped under **no clear equivalences**.
### Summary of Equivalent Groups
- Group 1: **\(-4a - 11\)** and **\(9 - 4(a + 5)\)**
- Group 2: **\(-6a - 15\)** and **\(-5(a + 3) - a\)**
- Group 3: **\(3a + 4b\)** and **\(5a + 3b - 2a + b\)**
- Group 4: **\(a + 14b\)** and **\(3a - 2(a - 7b)\)**
- Group 5: **\(5a + 12b\)** and **\(4(a + 3b) + a\)**
- Group 6: **\(11a + 4b\)** and **\(7a + 4(a + b)\)**
Let me know if you need further assistance or details!