Multliplication
Type – 01
1.a 
a =
2. a a a =
3. a a a a =
4. a a a a a =
5. a a a a a a =
6. b b =
7. b b b =
8. b b b b =
9. b b b b b =
10. b b b b b b =
11. m m =
12. m m m =
13. m m m m =
14. m m m m m =
15. m m m m m m =
16. y y =
17. y y y =
18. y y y y =
19. y y y y y =
20. y y y y y y =
Type – 02
1.a b =
2. a b c =
3. a b c a =
4. b a b a b =
5. a b c a b c =
6. b c =
7. b c b =
8. b a b b =
9. a b b b b =
10. a b b b c c =
11. m n =
12. m n m =
13. m n m m =
14. m n m n m =
15. m m n n m m =
16. b a =
17. b b c =
18. a b c d =
19. y y y y y =
20. a b a b c c =
Type – 03
1.a 2a =
2. a 2a a =
3. 2a 2a 2a a =
4. 2a 3a a 2a 2a =
5. a 3a 2a a 4a 2a =
6. 3b b =
7. 3b 2b 2b =
8. 2b 2b 3b 4b =
9. 4b 2b 3b b b =
10. 2b 3b 2b 2b 5b b =
11. 2m m =
12. m 3m m =
13. m 2m 3m 4m =
14. 2m m 2m m 3m =
15. m 2m 3m 5m 6m 4m =
16. 3y 2y =
17. 2y 3y 4y =
18. 2y 3y 4y 5y =
19. 2y 3y 5y 8y 6y =
20. 2y 5y 6y 7y 8y 3y =
Type – 04
1.2a b =
2. 2a 3b 2c =
3. 2a 3b 2c a =
4. b 2a b 3a 5b =
5. 2a 3b 5c a b c =
6. 5b 6c =
7. b 2c b =
8. 2b 3a 5b 4b =
9. 2a 3b 2b 5b 3b =
10. 2a 3b 3b 5b 2c 6c =
11. 3m 3n =
12. 2m 3n 5m =
13. 2m 3n 2m 5m =
14. 5m n 2m 5n m =
15. m 3m 3n n 2m m =
16. 5b 7a =
17. 2b 3b 2c =
18. 1a 2b 3c 4d =
19. 2y 3y 5y 6y 7y =
20. 2a 3b 4a 5b 6c 2c =
Type – 05
1.a2 a2 =
2. a2 a2 a2 =
3. a2 a2 a2 a2 =
4. a2 a2 a2 a2 a2 =
5. a2 a2 a2 a2 a2 a2 =
6. b2 b2 =
7. b2 b2 b2 =
8. b2 b2 b2 b2 =
9. b2 b2 b2 b2 b2 =
10. b2 b2 b2 b2 b2 b2 =
11. m2 m2 =
12. m2 m2 m2 =
13. m2 m2 m2 m2 =
14. m2 m2 m2 m2 m2 =
15. m2 m2 m2 m2 m2 m2 =
16. y2 y2 =
17. y2 y2 y2 =
18. y2 y2 y2 y2 =
19. y2 y2 y2 y2 y2 =
20. y2 y2 y2 y2 y2 y2 =
Type – 06
1. a2 b2 =
2. a2 b2 c2 =
3. a2 b2 c2 a2 =
4. b2 a2 b2 a2 b2 =
5. a2 b2 c2 a2 b2 c2 =
6. b2 c2 =
7. b2 c2 b2 =
8. b2 a2 b2 b2 =
9. a2 b2 b2 b2 b2 =
10. a2 b2 b2 b2 c2 c2 =
11. m2 n2 =
12. m2 n2 m2 =
13. m2 n2 m2 m2 =
14. m2 n2 m2 n2 m2 =
15. m2 m2 n2 n2 m2 m2 =
16. b2 a2 =
17. b2 b2 c2 =
18. a2 b2 c2 d2 =
19. y2 y2 y2 y2 y2 =
20. a2 b2 a2 b2 c2 c2 =
Type – 07
1.a2 2a2 =
2. a2 2a2 a2 =
3. 2a2 2a2 2a2 a2 =
4. 2a2 3a2 a2 2a2 2a2 =
5. a2 3a2 2a2 a2 4a2 2a2 =
6. 3b2 b2 =
7. 3b2 2b2 2b2 =
8. 2b2 2b2 3b2 4b2 =
9. 4b2 2b2 3b2 b2 b2 =
10. 2b2 3b2 2b2 2b2 5b2 b2 =
11. 2m2 m2 =
12. m2 3m2 m2 =
13. m2 2m2 3m2 4m2 =
14. 2m2 m2 2m2 m2 3m2 =
15. m2 2m2 3m2 5m2 6m2 4m2 =
16. 3y2 2y2 =
17. 2y2 3y2 4y2 =
18. 2y2 3y2 4y2 5y2 =
19. 2y2 3y2 5y2 8y2 6y2 =
20. 2y2 5y2 6y2 7y2 8y2 3y2 =
Type – 08
1. 2a2 b2 =
2. 2a2 3b2 2c2 =
3. 2a2 3b2 2c2 a2 =
4. b2 2a2 b2 3a2 5b2 =
5. 2a2 3b2 5c2 a2 b2 c2 =
6. 5b2 6c2 =
7. b2 2c2 b2 =
8. 2b2 3a2 5b2 4b2 =
9. 2a2 3b2 2b2 5b2 3b2 =
10. 2a2 3b2 3b2 5b2 2c2 6c2 =
11. 3m2 3n2 =
12. 2m2 3n2 5m2 =
13. 2m2 3n2 2m2 5m2 =
14. 5m2 n2 2m2 5n2 m2 =
15. m2 3m2 3n2 n2 2m2 m2 =
16. 5b2 7a2 =
17. 2b2 3b2 2c2 =
18. 1a2 2b2 3c2 4d2 =
19. 2y2 3y2 5y2 6y2 7y2 =
20. 2a2 3b2 4a2 5b2 6c2 2c2 =
Type – 09
1.a3 a3 =
2. a3 a3 a3 =
3. a3 a3 a3 a3 =
4. a3 a3 a3 a3 a3 =
5. a3 a3 a3 a3 a3 a3 =
6. b3 b3 =
7. b3 b3 b3 =
8. b3 b3 b3 b3 =
9. b3 b3 b3 b3 b3 =
10. b3 b3 b3 b3 b3 b3 =
11. m3 m3 =
12. m3 m3 m3 =
13. m3 m3 m3 m3 =
14. m3 m3 m3 m3 m3 =
15. m3 m3 m3 m3 m3 m3 =
16. y3 y3 =
17. y3 y3 y3 =
18. y3 y3 y3 y3 =
19. y3 y3 y3 y3 y3 =
20. y3 y3 y3 y3 y3 y3 =
Type – 10
1.a3 b3 =
2. a3 b3 c3 =
3. a3 b3 c3 a3 =
4. b3 a3 b3 a3 b3 =
5. a3 b3 c3 a3 b3 c3 =
6. b3 c3 =
7. b3 c3 b3 =
8. b3 a3 b3 b3 =
9. a3 b3 b3 b3 b3 =
10. a3 b3 b3 b3 c3 c3 =
11. m3 n3 =
12. m3 n3 m3 =
13. m3 n3 m3 m3 =
14. m3 n3 m3 n3 m3 =
15. m3 m3 n3 n3 m3 m3 =
16. b3 a3 =
17. b3 b3 c3 =
18. a3 b3 c3 d3 =
19. y3 y3 y3 y3 y3 =
20. a3 b3 a3 b3 c3 c3 =
Type – 11
1. a3 2a3 =
2. a3 2a3 a3 =
3. 2a3 2a3 2a3 a3 =
4. 2a3 3a3 a3 2a3 2a3 =
5. a3 3a3 2a3 a3 4a3 2a3 =
6. 3b3 b3 =
7. 3b3 2b3 2b3 =
8. 2b3 2b3 3b3 4b3 =
9. 4b3 2b3 3b3 b3 b3 =
10. 2b3 3b3 2b3 2b3 5b3 b3 =
11. 2m3 m3 =
12. m3 3m3 m3 =
13. m3 2m3 3m3 4m3 =
14. 2m3 m3 2m3 m3 3m3 =
15. m3 2m3 3m3 5m3 6m3 4m3 =
16. 3y3 2y3 =
17. 2y3 3y3 4y3 =
18. 2y3 3y3 4y3 5y3 =
19. 2y3 3y3 5y3 8y3 6y3 =
20. 2y3 5y3 6y3 7y3 8y3 3y3 =
Type – 12
1.2a3 b3 =
2. 2a3 3b3 2c3 =
3. 2a3 3b3 2c3 a3 =
4. b3 2a3 b3 3a3 5b3 =
5. 2a3 3b3 5c3 a3 b3 c3 =
6. 5b3 6c3 =
7. b3 2c3 b3 =
8. 2b3 3a3 5b3 4b3 =
9. 2a3 3b3 2b3 5b3 3b3 =
10. 2a3 3b3 3b3 5b3 2c3 6c3 =
11. 3m3 3n3 =
12. 2m3 3n3 5m3 =
13. 2m3 3n3 2m3 5m3 =
14. 5m3 n3 2m3 5n3 m3 =
15. m3 3m3 3n3 n3 2m3 m3 =
16. 5b3 7a3 =
17. 2b3 3b3 2c3 =
18. 1a3 2b3 3c3 4d3 =
19. 2y3 3y3 5y3 6y3 7y3 =
20. 2a3 3b3 4a3 5b3 6c3 2c3 =
Type – 13
1.a a2 a3 =
2. 2a 3a2 4a3 =
3. a2 a2 a3 a3 =
4. 2a2 3a2 4a3 =
5. 2a3 3a2 4a3 =
6. 2a2 a2 3a3 4a3 =
7. b b2 b3 =
8. 2b 3b2 4c3 =
9. b2 a2 b3 a3 =
10. 2c2 3b2 4a3 =
11. 2c3 3a2 4b3 =
12. 2b2 c2 3a3 4b3 =
13. 2m3 3m3 3n3 3n3 2m3 2m3 =
14. 2b3 3a3 2c3 =
15. 1a3 2c3 3c3 4a3 =
16. 2y3 3y3 5y3 6b3 7b3 =
17. 2a3 3a3 4b3 5b3 6c3 2c3 =
18. 2a3 3b3 4a3 5b3 =
19. 2b3 3b3 5c3 8c3 6a3 =
20. 2a3 5b3 6c3 7a3 8b3 3c3 =
Type – 14
If a = 1 , b = 2 , m = 3 & y = 4 Find
1.a a =
2. a a a =
3. a a a a =
4. a a a a a =
5. a a a a a a =
6. b b =
7. b b b =
8. b b b b =
9. b b b b b =
10. b b b b b b =
11. m m =
12. m m m =
13. m m m m =
14. m m m m m =
15. m m m m m m =
16. y y =
17. y y y =
18. y y y y =
19. y y y y y =
20. y y y y y y =
Type – 15
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a b =
2. a b c =
3. a b c a =
4. b a b a b =
5. a b c a b c =
6. b c =
7. b c b =
8. b a b b =
9. a b b b b =
10. a b b b c c =
11. m n =
12. m n m =
13. m n m m =
14. m n m n m =
15. m m n n m m =
16. b a =
17. b b c =
18. a b c d =
19. y y y y y =
20. a b a b c c =
Type – 16
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a 2a =
2. a 2a a =
3. 2a 2a 2a a =
4. 2a 3a a 2a 2a =
5. a 3a 2a a 4a 2a =
6. 3b b =
7. 3b 2b 2b =
8. 2b 2b 3b 4b =
9. 4b 2b 3b b b =
10. 2b 3b 2b 2b 5b b =
11. 2m m =
12. m 3m m =
13. m 2m 3m 4m =
14. 2m m 2m m 3m =
15. m 2m 3m 5m 6m 4m =
16. 3y 2y =
17. 2y 3y 4y =
18. 2y 3y 4y 5y =
19. 2y 3y 5y 8y 6y =
20. 2y 5y 6y 7y 8y 3y =
Type – 17
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.2a b =
2. 2a 3b 2c =
3. 2a 3b 2c a =
4. b 2a b 3a 5b =
5. 2a 3b 5c a b c =
6. 5b 6c =
7. b 2c b =
8. 2b 3a 5b 4b =
9. 2a 3b 2b 5b 3b =
10. 2a 3b 3b 5b 2c 6c =
11. 3m 3n =
12. 2m 3n 5m =
13. 2m 3n 2m 5m =
14. 5m n 2m 5n m =
15. m 3m 3n n 2m m =
16. 5b 7a =
17. 2b 3b 2c =
18. 1a 2b 3c 4d =
19. 2y 3y 5y 6y 7y =
20. 2a 3b 4a 5b 6c 2c =
Type – 18
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a2 a2 =
2. a2 a2 a2 =
3. a2 a2 a2 a2 =
4. a2 a2 a2 a2 a2 =
5. a2 a2 a2 a2 a2 a2 =
6. b2 b2 =
7. b2 b2 b2 =
8. b2 b2 b2 b2 =
9. b2 b2 b2 b2 b2 =
10. b2 b2 b2 b2 b2 b2 =
11. m2 m2 =
12. m2 m2 m2 =
13. m2 m2 m2 m2 =
14. m2 m2 m2 m2 m2 =
15. m2 m2 m2 m2 m2 m2 =
16. y2 y2 =
17. y2 y2 y2 =
18. y2 y2 y2 y2 =
19. y2 y2 y2 y2 y2 =
20. y2 y2 y2 y2 y2 y2 =
Type – 19
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1. a2 b2 =
2. a2 b2 c2 =
3. a2 b2 c2 a2 =
4. b2 a2 b2 a2 b2 =
5. a2 b2 c2 a2 b2 c2 =
6. b2 c2 =
7. b2 c2 b2 =
8. b2 a2 b2 b2 =
9. a2 b2 b2 b2 b2 =
10. a2 b2 b2 b2 c2 c2 =
11. m2 n2 =
12. m2 n2 m2 =
13. m2 n2 m2 m2 =
14. m2 n2 m2 n2 m2 =
15. m2 m2 n2 n2 m2 m2 =
16. b2 a2 =
17. b2 b2 c2 =
18. a2 b2 c2 d2 =
19. y2 y2 y2 y2 y2 =
20. a2 b2 a2 b2 c2 c2 =
Type – 20
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a2 2a2 =
2. a2 2a2 a2 =
3. 2a2 2a2 2a2 a2 =
4. 2a2 3a2 a2 2a2 2a2 =
5. a2 3a2 2a2 a2 4a2 2a2 =
6. 3b2 b2 =
7. 3b2 2b2 2b2 =
8. 2b2 2b2 3b2 4b2 =
9. 4b2 2b2 3b2 b2 b2 =
10. 2b2 3b2 2b2 2b2 5b2 b2 =
11. 2m2 m2 =
12. m2 3m2 m2 =
13. m2 2m2 3m2 4m2 =
14. 2m2 m2 2m2 m2 3m2 =
15. m2 2m2 3m2 5m2 6m2 4m2 =
16. 3y2 2y2 =
17. 2y2 3y2 4y2 =
18. 2y2 3y2 4y2 5y2 =
19. 2y2 3y2 5y2 8y2 6y2 =
20. 2y2 5y2 6y2 7y2 8y2 3y2 =
Type – 21
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1. 2a2 b2 =
2. 2a2 3b2 2c2 =
3. 2a2 3b2 2c2 a2 =
4. b2 2a2 b2 3a2 5b2 =
5. 2a2 3b2 5c2 a2 b2 c2 =
6. 5b2 6c2 =
7. b2 2c2 b2 =
8. 2b2 3a2 5b2 4b2 =
9. 2a2 3b2 2b2 5b2 3b2 =
10. 2a2 3b2 3b2 5b2 2c2 6c2 =
11. 3m2 3n2 =
12. 2m2 3n2 5m2 =
13. 2m2 3n2 2m2 5m2 =
14. 5m2 n2 2m2 5n2 m2 =
15. m2 3m2 3n2 n2 2m2 m2 =
16. 5b2 7a2 =
17. 2b2 3b2 2c2 =
18. 1a2 2b2 3c2 4d2 =
19. 2y2 3y2 5y2 6y2 7y2 =
20. 2a2 3b2 4a2 5b2 6c2 2c2 =
Type – 22
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a3 a3 =
2. a3 a3 a3 =
3. a3 a3 a3 a3 =
4. a3 a3 a3 a3 a3 =
5. a3 a3 a3 a3 a3 a3 =
6. b3 b3 =
7. b3 b3 b3 =
8. b3 b3 b3 b3 =
9. b3 b3 b3 b3 b3 =
10. b3 b3 b3 b3 b3 b3 =
11. m3 m3 =
12. m3 m3 m3 =
13. m3 m3 m3 m3 =
14. m3 m3 m3 m3 m3 =
15. m3 m3 m3 m3 m3 m3 =
16. y3 y3 =
17. y3 y3 y3 =
18. y3 y3 y3 y3 =
19. y3 y3 y3 y3 y3 =
20. y3 y3 y3 y3 y3 y3 =
Type – 23
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a3 b3 =
2. a3 b3 c3 =
3. a3 b3 c3 a3 =
4. b3 a3 b3 a3 b3 =
5. a3 b3 c3 a3 b3 c3 =
6. b3 c3 =
7. b3 c3 b3 =
8. b3 a3 b3 b3 =
9. a3 b3 b3 b3 b3 =
10. a3 b3 b3 b3 c3 c3 =
11. m3 n3 =
12. m3 n3 m3 =
13. m3 n3 m3 m3 =
14. m3 n3 m3 n3 m3 =
15. m3 m3 n3 n3 m3 m3 =
16. b3 a3 =
17. b3 b3 c3 =
18. a3 b3 c3 d3 =
19. y3 y3 y3 y3 y3 =
20. a3 b3 a3 b3 c3 c3 =
Type – 24
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1. a3 2a3 =
2. a3 2a3 a3 =
3. 2a3 2a3 2a3 a3 =
4. 2a3 3a3 a3 2a3 2a3 =
5. a3 3a3 2a3 a3 4a3 2a3 =
6. 3b3 b3 =
7. 3b3 2b3 2b3 =
8. 2b3 2b3 3b3 4b3 =
9. 4b3 2b3 3b3 b3 b3 =
10. 2b3 3b3 2b3 2b3 5b3 b3 =
11. 2m3 m3 =
12. m3 3m3 m3 =
13. m3 2m3 3m3 4m3 =
14. 2m3 m3 2m3 m3 3m3 =
15. m3 2m3 3m3 5m3 6m3 4m3 =
16. 3y3 2y3 =
17. 2y3 3y3 4y3 =
18. 2y3 3y3 4y3 5y3 =
19. 2y3 3y3 5y3 8y3 6y3 =
20. 2y3 5y3 6y3 7y3 8y3 3y3 =
Type – 25
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.2a3 b3 =
2. 2a3 3b3 2c3 =
3. 2a3 3b3 2c3 a3 =
4. b3 2a3 b3 3a3 5b3 =
5. 2a3 3b3 5c3 a3 b3 c3 =
6. 5b3 6c3 =
7. b3 2c3 b3 =
8. 2b3 3a3 5b3 4b3 =
9. 2a3 3b3 2b3 5b3 3b3 =
10. 2a3 3b3 3b3 5b3 2c3 6c3 =
11. 3m3 3n3 =
12. 2m3 3n3 5m3 =
13. 2m3 3n3 2m3 5m3 =
14. 5m3 n3 2m3 5n3 m3 =
15. m3 3m3 3n3 n3 2m3 m3 =
16. 5b3 7a3 =
17. 2b3 3b3 2c3 =
18. 1a3 2b3 3c3 4d3 =
19. 2y3 3y3 5y3 6y3 7y3 =
20. 2a3 3b3 4a3 5b3 6c3 2c3 =
Type – 26
If a = 1 , b = 2 , c = 3 , d = 4 , m = 5 , n = 6 & y = 7 Find
1.a a2 a3 =
2. 2a 3a2 4a3 =
3. a2 a2 a3 a3 =
4. 2a2 3a2 4a3 =
5. 2a3 3a2 4a3 =
6. 2a2 a2 3a3 4a3 =
7. b b2 b3 =
8. 2b 3b2 4c3 =
9. b2 a2 b3 a3 =
10. 2c2 3b2 4a3 =
11. 2c3 3a2 4b3 =
12. 2b2 c2 3a3 4b3 =
13. 2m3 3m3 3n3 3n3 2m3 2m3 =
14. 2b3 3a3 2c3 =
15. 1a3 2c3 3c3 4a3 =
16. 2y3 3y3 5y3 6b3 7b3 =
17. 2a3 3a3 4b3 5b3 6c3 2c3 =
18. 2a3 3b3 4a3 5b3 =
19. 2b3 3b3 5c3 8c3 6a3 =
20. 2a3 5b3 6c3 7a3 8b3 3c3 =
Type – 27 (Multliplication)
1.2a, -a =
2. 3a, -a & 4a =
3. a, 5a , -6a & 4a =
4. 3a, 8a, -7a, -6a & 5a =
5. 6a, 4a, -7a, -8a , -9a & 10a =
6. 10b, -5b =
7. 5b, -6b & 3b =
8. 5b, -6b, -7b & 8b =
9. -8b, 9b, -2b, -3b, -7b =
10. -10b, 2b, 8b, -9b, 7b & -11b =
11. -6m, 8m =
12. -8m, -9m & 7m =
13. 8m, -10m, -12m & 15m =
14. 9m, 7m, -8m, -9m & 12m =
15. 9m, 10m, 3m , 4m, -9m & 7m =
16. 10y , -8y =
17. 3y , -4y & 6y =
18. -9y , 8y, -7y & -4y =
19. 10y, -11y, -12y , 9y & 10y =
20. 6y, -5y, 4y, 3y , 2y & -y =
Type – 28 (Multliplication)
1.5a , 3b =
2. 3a, -2b & 4c =
3. 6a, 3b, 4c & -8a =
4. -5b, 6a, -8b, -7a & -5b =
5. 3a, -2b, -c, -4a, 8b & 7c =
6. -9b, 8c =
7. -6b, -10c & 9b =
8. -10b, 9a, 8b & -7b =
9. 2a, -3b, -5b, -4b & 8b =
10. -8a, 7b, 5b, 4b, -3c & 2c =
11. -8m, 3n =
12. -5m, -6n & 8m =
13. 10m, -11n, -12m & 13m =
14. 8m, -9n, 7m, 3n & 10m =
15. 6m, -10m, -15n, 14n, 10m & 8m =
16. 8b , -9a =
17. 9b, -7b & 6c =
18. 5a, -6b, -8c & 7d =
19. -8y, 10y, 11y, 16y & 17y =
20. -6a, 3b, -2a, 8b, 7c & -9c =
Type – 29 (Multliplication)
1. 8a, -2a =
2. 6a, -10a & 12a =
3. 2a, 8a, -2a & a =
4. -10a, -12a, 14a, -16a & 18a =
5. 10a, 3a, -2a, -10a, -4a & -2a =
6. 14b, -16b =
7. -3b, 2b & -2b =
8. -8b, 9b, 7b & -10b =
9. -4b, -2b, -3b, -b & -b =
10. -2b, 5b, -2b, 2b, 5b & b =
11. 15m, -m =
12. -3m, 8m & -7m =
13. 8m, -12m, 13m & 14m =
14. 15m, -14m, -12m, -15m & -10m =
15. 10m, 20m, -30m, -5m, -6m & -4m =
16. -3y, -2y =
17. -2y, -3y & -4y =
18. -2y, -3y, -4y, -5y =
19. -10y, 30y, 25y, -18y & -16y =
20. 2y, -5y, -6y, -7y, -8y & 3y =
Type – 30 (Multliplication)
1.5a2, -a2 =
2. -6a2, 5a2 & 8a2 =
3. 6a2, -8a2, 7a2 & 8a2 =
4. 5a2, -2a2, -3a2, -6a2 & 8a2 =
5. 8a2, 2a2, 8a2, 7a2, -10a2 & 11a2 =
6. 10b2, 6b2 =
7. 6b2, -3b2 & -2b2 =
8. -8b2, 2b2, -10b2 & -8b2 =
9. -8b2, 6b2, 10b2, -4b2 & -8b2 =
10. 6b2, -5b2, -3b2, -4b2, -7b2 & 8b2 =
11. -9m2 , 2m2 =
12. -3m2 , 2m2 & 8m2 =
13. 8m2 , -10m2 , -9m2 & 7m2 =
14. 8m2 , -7m2 , -9m2 , -5m2 & -6m2 =
15. 8m2 , -7m2 , -6m2 , 7m2 , 8m2 & 9m2 =
16. -8y2 , -5y2 =
17. -5y2 , -4y2 & 6y2 =
18. 6y2 , -7y2 , -8y2 & -5y2 =
19. 8y2 , 9y2 , 4y2 , 5y2 & 6y2 =
20. -9y2 , 7y2 , -8y2 , -7y2 , -5y2 & -6y2 =
Type – 31 (Multliplication)
1.-6a2 , 5b2 =
2. -6a2 , 5b2 & 4c2 =
3. -10a2 , 5b2 , 6c2 & -9a2 =
4. 8b2 , 5a2 , -6b2 , -5a2 & 4b2 =
5. 10a2, 12b2 , 6c2 , 8a2 , 7b2 & 9c2 =
6. 9b2 , -2c2 =
7. 3b2 , 2c2 & -8b2 =
8. -9b2 , -2a2 , -3b2 & -10b2 =
9. 10a2 , -10b2 , 9b2 , 8b2 & -4b2 =
10. 4a2 , 3b2 , -2b2 , 8b2 , -7c2 & 5c2 =
11. -6m2 , -5n2 =
12. -5m2 , -8n2 & -7m2 =
13. -8m2 , -5n2 , -7m2 & -7m2 =
14. 6m2 , 7n2 , 8m2 , 5n2 & 6m2 =
15. 6m2 , 2m2 , 3n2 , 4n2 , 2m2 & 3m2 =
16. 3b2 , -8a2 =
17. 8b2 , 3b2 & -4c2 =
18. 8a2 , 2b2 , 3c2 & 4d2 =
19. 8y2 , 9y2 , 7y2 , 3y2 & -4y2 =
20. 10a2 , 3b2 , 5a2 , 4b2 , -8c2 & -9c2 =
Type – 32 (Multliplication)
1.10a2 , 12a2 =
2. 6a2 , 2a2 & -8a2 =
3. 12a2 , 12a2 , 13a2 & 10a2 =
4. 9a2 , 8a2 , 8a2 , 7a2 & -5a2 =
5. 6a2 , 7a2 , -8a2 , 9a2 , 7a2 & 10a2 =
6. 12b2 , -10b2 =
7. 9b2 , -12b2 & 12b2 =
8. -10b2 , 8b2 , -7b2 & 8b2 =
9. 9b2 , 8b2 , 7b2 , 4b2 & -3b2 =
10. -7b2 , -9b2 , -7b2 , 6b2 , 8b2 & 7b2 =
11. 12m2 , 10m2 =
12. 10m2 , 3m2 & 5m2 =
13. 14m2 , 12m2 , -3m2 & -4m2 =
14. 12m2 , 10m2 , 2m2 , 8m2 & -9m2 =
15. 5m2 , 12m2 , 3m2 , 5m2 , 6m2 & 4m2 =
16. 13y2 , 12y2 =
17. 12y2 , 3y2 & 4y2 =
18. 6y2 , 3y2 , 4y2 & 5y2 =
19. 2y2 , 3y2 , 5y2 , 8y2 & 6y2 =
20. 2y2 , 5y2 , 6y2 , 7y2 , 8y2 & 3y2 =
Type – 33 (Multliplication)
1. 10a2 , 8b2 =
2. 2a2 , 3b2 & -2c2 =
3. 2a2 , 3b2 , 2c2 & -a2 =
4. b2 , 2a2 , b2 , 3a2 & -5b2 =
5. 2a2 , 3b2 , 5c2 , -a2 , b2 & -c2 =
6. 5b2 , 6c2 =
7. 6b2 , 2c2 & 5b2 =
8. 2b2 , -3a2 , 5b2 & -4b2 =
9. 2a2 , -3b2 , -2b2 , -5b2 & -3b2 =
10. 2a2 , 3b2 , 3b2 , 5b2 , 2c2 & -6c2 =
11. 3m2 , 3n2 =
12. 2m2 , 3n2 & -5m2 =
13. 2m2 , 3n2 , -2m2 & -5m2 =
14. 5m2 , n2 , 2m2 , -5n2 & -m2 =
15. m2 , 3m2 , -3n2 , n2 , -2m2 & -m2 =
16. 5b2 , 7a2 =
17. 2b2 , 3b2 & 2c2 =
18. 1a2 , 2b2 , 3c2 & 4d2 =
19. 2y2 , 3y2 , 5y2 , 6y2 & 7y2 =
20. 2a2 , 3b2 , -4a2 , 5b2 , 6c2 & -2c2 =
Type – 34 (Multliplication)
1.5a , 6a2 & 7a3 =
2. 2a , 3a2 & 4a3 =
3. a2 , a2 , a3 & -a3 =
4. 2a2 , 3a2 & 4a3 =
5. 2a3 , 3a2 & 4a3 =
6. 2a2 , a2 , 3a3 & 4a3 =
7. 5b , 6b2 & b3 =
8. 2b , 3b2 & 4c3 =
9. b2 , a2 , b3 & -a3 =
10.2c2 , 3b2 7 4a3 =
11. 2c3 , 3a2 & 4b3 =
12. 2b2 , c2 , 3a3 & -4b3 =
13. 2m3 , 3m3 , 3n3 , 3n3 , -2m3 & -2m3 =
14. 2b3 , 3a3 & 2c3 =
15. 1a3 , 2c3 , 3c3 & -4a3 =
16. 2y3 , 3y3 , 5y3 , 6b3 & 7b3 =
17. 2a3 , 3a3 , 4b3 , 5b3 , -6c3 & -2c3 =
18. 2a3 , 3b3 , 4a3 & -5b3 =
19. 2b3 , 3b3 , -5c3 , -8c3 & -6a3 =
20. 2a3 , 5b3 , 6c3 , -7a3 , –8b3 & -3c3 =
Type – 35 (Multliplication)
1.( a + b ) a =
2. ( b+ c ) a =
3. ( c + a ) a =
4. ( a + b ) b =
5. ( b+ c ) b =
6. ( c + a ) b =
7. ( a + b ) c =
8. ( b+ c ) c =
9. ( c + a ) c =
10. (a + b ) (a + b ) =
11. (b + c ) (b + c ) =
12. (c + a ) (c + a ) =
Type – 36 (Multliplication)
1.( 2a + 3b ) 2a =
2. ( 3b+ 4c ) 2a =
3. ( 2c + 5a ) 2a =
4. ( 3a + 4b ) 2b =
5. ( 3b+ 4c ) 2b =
6. ( 3c + 8a ) 2b =
7. ( 4a + 5b ) 2c =
8. ( 6b + 5c ) 2c =
9. ( 3c + 4a ) 6c =
10. (5a + 2b ) (2a + 3b ) =
11. (2b + c ) (2b + c ) =
12. (5c + 4a ) (5c + 4a ) =
Type – 37 (Multliplication)
1.( a + b + c ) a =
2. ( b+ c + a ) a =
3. ( c + a + b ) a =
4. ( a + b + c ) b =
5. ( b+ c + a) b =
6. ( c + a + b ) b =
7. ( a + b + c ) c =
8. ( b+ c+ a ) c =
9. ( c + a + b ) c =
10. (a + b + c ) (a + b ) =
11. (b + c + a ) (b + c ) =
12. (c + a + b ) (c + a ) =
Type – 38 (Multliplication)
1.( 2a + 3b + 4c ) 2a =
2. ( 3b+ 2c + 5a ) 2a =
3. ( 3c + 2a + 5b ) 4a =
4. ( 2a + 3b + 4c ) 6b =
5. ( 2b+ 3c + 4a) 5b =
6. ( 3c + 2a + 5b ) 8b =
7. ( 2a + 3b + 5c ) 2c =
8. ( 2b+ 3c+ 4a ) 2c =
9. ( 2c + 3a + 4b ) 5c =
10. (2a + 3b + 4c ) (2a + 3b ) =
11. (3b + 4c + 5a ) (2b + 3c ) =
12. (3c + 4a + 5b ) (2c + 3a ) =
Type – 39 (Multliplication)
1. (a + b + c ) (a + b + c ) =
2. (b + c + a ) (b + c + a ) =
3. (c + a + b ) (c + a + b ) =
4. (2a + 3b + 4c ) (2a + 3b + 4c ) =
5. (3b + 4c + 5a ) (3b + 4c + 5a ) =
6. (4c + 5a + 6b ) (4c + 5a + 6b ) =
Type – 40 (Multliplication)
1.( a – b ) a =
2. ( b – c ) a =
3. ( c – a ) a =
4. ( a – b ) b =
5. ( b – c ) b =
6. ( c – a ) b =
7. ( a – b ) c =
8. ( b – c ) c =
9. ( c – a ) c =
10. (a – b ) (a – b ) =
11. (b – c ) (b – c ) =
12. (c – a ) (c – a ) =
Type – 41 (Multliplication)
1.( 2a – 3b ) 2a =
2. ( 3b – 4c ) 2a =
3. ( 2c – 5a ) 2a =
4. ( 3a – 4b ) 2b =
5. ( 3b – 4c ) 2b =
6. ( 3c – 8a ) 2b =
7. ( 4a – 5b ) 2c =
8. ( 6b – 5c ) 2c =
9. ( 3c – 4a ) 6c =
10. (5a – 2b ) (2a – 3b ) =
11. (2b – c ) (2b – c ) =
12. (5c – 4a ) (5c – 4a ) =
Type – 42 (Multliplication)
1.( a + b – c ) a =
2. ( b+ c – a ) a =
3. ( c + a – b ) a =
4. ( a + b – c ) b =
5. ( b+ c – a) b =
6. ( c + a – b ) b =
7. ( a + b – c ) c =
8. ( b+ c – a ) c =
9. ( c + a – b ) c =
10. (a + b – c ) (a – b ) =
11. (b + c – a ) (b – c ) =
12. (c + a – b ) (c – a ) =
Type – 43 (Multliplication)
1.( 2a + 3b – 4c ) 2a =
2. ( 3b+ 2c – 5a ) 2a =
3. ( 3c + 2a – 5b ) 4a =
4. ( 2a + 3b – 4c ) 6b =
5. ( 2b+ 3c – 4a) 5b =
6. ( 3c + 2a – 5b ) 8b =
7. ( 2a + 3b – 5c ) 2c =
8. ( 2b + 3c – 4a ) 2c =
9. ( 2c + 3a – 4b ) 5c =
10. (2a + 3b – 4c ) (2a – 3b ) =
11. (3b + 4c – 5a ) (2b – 3c ) =
12. (3c + 4a – 5b ) (2c – 3a ) =
Type – 44 (Multliplication)
1. (a + b – c ) (a + b – c ) =
2. (b + c – a ) (b + c – a ) =
3. (c + a – b ) (c + a – b ) =
4. (2a + 3b – 4c ) (2a + 3b – 4c ) =
5. (3b + 4c – 5a ) (3b + 4c – 5a ) =
6. (4c + 5a – 6b ) (4c + 5a – 6b ) =
Type – 45 (Multliplication)
1.( a – b + c ) a =
2. ( b – c + a ) a =
3. ( c – a + b ) a =
4. ( a – b + c ) b =
5. ( b – c + a) b =
6. ( c – a + b ) b =
7. ( a – b + c ) c =
8. ( b – c+ a ) c =
9. ( c – a + b ) c =
10. (a – b + c ) (a – b ) =
11. (b – c + a ) (b – c ) =
12. (c – a + b ) (c – a ) =
Type – 46 (Multliplication)
1.( 2a – 3b + 4c ) 2a =
2. ( 3b – 2c + 5a ) 2a =
3. ( 3c – 2a + 5b ) 4a =
4. ( 2a – 3b + 4c ) 6b =
5. ( 2b – 3c + 4a) 5b =
6. ( 3c – 2a + 5b ) 8b =
7. ( 2a – 3b + 5c ) 2c =
8. ( 2b – 3c+ 4a ) 2c =
9. ( 2c – 3a + 4b ) 5c =
10. (2a – 3b + 4c ) (2a – 3b ) =
11. (3b – 4c + 5a ) (2b – 3c ) =
12. (3c – 4a + 5b ) (2c – 3a ) =
Type – 47 (Multliplication)
1. (a – b + c ) (a – b + c ) =
2. (b – c + a ) (b – c + a ) =
3. (c – a + b ) (c – a + b ) =
4. (2a – 3b + 4c ) (2a – 3b + 4c ) =
5. (3b – 4c + 5a ) (3b – 4c + 5a ) =
6. (4c – 5a + 6b ) (4c – 5a + 6b ) =
Type – 48 (Multliplication)
1.( a – b – c ) a =
2. ( b – c – a ) a =
3. ( c – a – b ) a =
4. ( a – b – c ) b =
5. ( b – c – a) b =
6. ( c – a – b ) b =
7. ( a – b – c ) c =
8. ( b – c – a ) c =
9. ( c – a – b ) c =
10. (a – b – c ) (a – b ) =
11. (b – c – a ) (b – c ) =
12. (c – a – b ) (c – a ) =
Type – 49 (Multliplication)
1.( 2a – 3b – 4c ) 2a =
2. ( 3b – 2c – 5a ) 2a =
3. ( 3c – 2a – 5b ) 4a =
4. ( 2a – 3b – 4c ) 6b =
5. ( 2b – 3c – 4a) 5b =
6. ( 3c – 2a – 5b ) 8b =
7. ( 2a – 3b – 5c ) 2c =
8. ( 2b – 3c – 4a ) 2c =
9. ( 2c – 3a – 4b ) 5c =
10. (2a – 3b – 4c ) (2a – 3b ) =
11. (3b – 4c – 5a ) (2b – 3c ) =
12. (3c – 4a – 5b ) (2c – 3a ) =
Type – 50 (Multliplication)
1. (a – b – c ) (a – b – c ) =
2. (b – c – a ) (b – c – a ) =
3. (c – a – b ) (c – a – b ) =
4. (2a – 3b – 4c ) (2a – 3b – 4c ) =
5. (3b – 4c – 5a ) (3b – 4c – 5a ) =
6. (4c – 5a – 6b ) (4c – 5a – 6b ) =
Type – 51 ( Proved that )
1.( x + a ) ( x + b ) = x2 + (a + b ) x + ab
2. ( x + a ) ( x – b ) = x2 + (a – b ) x – ab
3. ( x – a ) ( x + b ) = x2 – (a + b ) x – ab
4. ( x – a ) ( x – b ) = x2 – (a + b ) x + ab
5. ( a + b )2 = a2 + 2ab + b2
= ( a – b )2 + 4ab
6. ( a – b )2 = a2 – 2ab + b2
= ( a + b )2 – 4ab
7. ( a + b )2 + ( a – b )2 = 2 ( a2 + b2 )
8. ( a + b )2 – ( a – b )2 = 4ab
9. a2 + b2 = ( a + b )2 – 2ab
= ( a – b )2 + 2ab
10. a2 – b2 = ( a + b ) ( a – b )
11. ( a + b + c )2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
12. ( a + b – c )2 = a2 + b2 + c2 + 2ab – 2bc – 2ca
13. ( a – b + c )2 = a2 + b2 + c2 – 2ab – 2bc + 2ca
14. ( a – b – c )2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
15. ( a + b + c )3 = a3 + b3 + c3 + 3 ( a + b ) ( b + c ) ( c + a )
16. ( a + b – c )3 = a3 + b3 – c3 – 3 ( a + b ) ( b – c ) ( c – a )
17. ( a – b + c )3 = a3 – b3 + c3 – 3 ( a – b ) ( b – c ) ( c + a )
18. ( a – b – c )3 = a3 – b3 – c3 + 3 ( a – b ) ( b + c ) ( c – a )
19. ( a + b )3 = a3 + b3 + 3ab ( a + b )
20. ( a – b )3 = a3 – b3 – 3ab ( a – b )
21. a3 + b3 = ( a + b )3 – 3ab ( a + b )
= ( a + b ) ( a2 – ab + b2 )
22. a3 – b3 = ( a – b )3 + 3ab ( a – b )
= ( a – b ) ( a2 + ab + b2 )