Factorization
1.(x + a)( x + b) = x2 + (a + b) x + ab
1.( x + 3 ) ( x + 5 ) =
2. ( x + 6 ) ( x + 4 ) =
3. ( x + 3 ) ( x + 4 ) =
4. ( x + 10 ) ( x + 11 ) =
5. ( x + 8 ) ( x + 9 ) =
6. ( x + 9 ) ( x + 3 ) =
7. ( x + 2 ) ( x + 4 ) =
8. ( x + 5 ) ( x + 6 ) =
9. ( x + 12 ) ( x + 14 ) =
10. ( x + 12 ) ( x + 10 ) =
2. (x + a) (x – b) = x2 + (a – b) x – ab
1.( x + 5 ) ( x – 3 ) =
2. ( x + 6 ) ( x – 4 ) =
3. ( x + 8 ) ( x – 4 ) =
4. ( x + 12 ) ( x – 11 ) =
5. ( x + 10 ) ( x – 9 ) =
6. ( x + 9 ) ( x – 3 ) =
7. ( x + 8 ) ( x – 4 ) =
8. ( x + 7 ) ( x – 6 ) =
9. ( x + 15 ) ( x – 14 ) =
10. ( x + 12 ) ( x – 10 ) =
3. (x – a) (x + b) = x2 – (a – b) x – ab
1.( x – 3 ) ( x + 5 ) =
2. ( x – 6 ) ( x + 4 ) =
3. ( x – 3 ) ( x + 4 ) =
4. ( x – 10 ) ( x + 11 ) =
5. ( x – 8 ) ( x + 9 ) =
6. ( x – 9 ) ( x + 3 ) =
7. ( x – 2 ) ( x + 4 ) =
8. ( x – 5 ) ( x + 6 ) =
9. ( x – 12 ) ( x + 14 ) =
10. ( x – 12 ) ( x + 10 ) =
4. (x – a) (x – b) = x2 – (a + b) x + ab
1.( x – 3 ) ( x – 5 ) =
2. ( x – 6 ) ( x – 4 ) =
3. ( x – 3 ) ( x – 4 ) =
4. ( x – 10 ) ( x – 11 ) =
5. ( x – 8 ) ( x – 9 ) =
6. ( x – 9 ) ( x – 3 ) =
7. ( x – 2 ) ( x – 4 ) =
8. ( x – 5 ) ( x – 6 ) =
9. ( x – 12 ) ( x – 14 ) =
10. ( x – 12 ) ( x – 10 ) =
5. (a + b)2 = a2 + 2ab + b2
= ( a – b )2 + 4ab
1. (2a + 3b )2 =
2. (a + 3b )2 =
3. (2a + b )2 =
4. (3a + 4b )2 =
5. (5a + 6b )2 =
6. (8a + 9b )2 =
7. (2a + 5b )2 =
8. (10a + 3b )2 =
9. (12a + 10b )2 =
10. (8a + 10b )2 =
6. ( a – b )2 = a2 – 2ab + b2
= ( a + b )2 – 4ab
1. (2a – 3b )2 =
2. (a – 3b )2 =
3. (2a – b )2 =
4. (3a – 4b )2 =
5. (5a – 6b )2 =
6. (8a – 9b )2 =
7. (2a – 5b )2 =
8. (10a – 3b )2 =
9. (12a – 10b )2 =
10. (8a – 10b )2 =
7. (a + b)2 + (a – b)2 = 2 (a2 + b2)
1.(2a + 3b)2 + ( 2a – 3b)2 =
2. (3a + 4b)2 + (3a – 4b)2 =
3. (5a + 4b)2 + (5a – 4b)2 =
4. (6a + 5b)2 + (6a – 5b)2 =
5. (8a + 5b)2 + (8a – 5b)2 =
6. (9a + 8b)2 + (9a – 8b)2 =
7. (10a + 5b)2 + (10a – 5b)2 =
8. (6a + 2b)2 + (6a – 2b)2 =
9. (12a + 10b)2 + (12a – 10b)2 =
10. (10a + 6b)2 + ( 10a – 6b)2 =
8. ( a + b )2 – ( a – b )2 = 4ab
1.(2a + 3b)2 – ( 2a – 3b)2 =
2. (3a + 4b)2 – (3a – 4b)2 =
3. (5a + 4b)2 – (5a – 4b)2 =
4. (6a + 5b)2 – (6a – 5b)2 =
5. (8a + 5b)2 – (8a – 5b)2 =
6. (9a + 8b)2 – (9a – 8b)2 =
7. (10a + 5b)2 – (10a – 5b)2 =
8. (6a + 2b)2 – (6a – 2b)2 =
9. (12a + 10b)2 – (12a – 10b)2 =
10. (10a + 6b)2 – ( 10a – 6b)2 =
9. a2 + b2 = ( a + b )2 – 2ab
= ( a – b )2 + 2ab
1.(2a)2 + (3b)2 =
2. (3a)2 + (4b)2 =
3. (5a)2 + (4b)2 =
4. (6a)2 + (4b)2 =
5. (8a)2 + (5b)2 =
6. (10a)2 + (5b)2 =
7. (10a)2 + (b)2 =
8. (12a)2 + (10b)2 =
9. (8a)2 + (7b)2 =
10. (a)2 + (3b)2 =
10. a2 – b2 = ( a + b ) ( a – b )
1.(2a)2 – (b)2 =
2. (3a)2 – (b)2 =
3. (5a)2 – (4b)2 =
4. (6a)2 – (4b)2 =
5. (8a)2 – (5b)2 =
6. (10a)2 – (5b)2 =
7. (10a)2 – (b)2 =
8. (12a)2 – (10b)2 =
9. (8a)2 – (7b)2 =
10. (9a)2 – (3b)2 =
11. ( a + b + c )2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
1.(2a + 3b + 4c)2 =
2. (a + 3b + 4c)2 =
3. (2a + b + 4c)2 =
4. (2a + 3b + c)2 =
5. (3a + 4b + 5c)2 =
6. (5a + 6b + 7c)2 =
7. (8a + 9b + 10c)2 =
8. (2a + 3b + 4c)2 =
9. (10a + 8b + 3c)2 =
10. (8a + 6b + 4c)2 =
12. ( a + b – c )2 = a2 + b2 + c2 + 2ab – 2bc – 2ca
1.(2a + 3b – 4c)2 =
2. (a + 3b – 4c)2 =
3. (2a + b – 4c)2 =
4. (2a + 3b – c)2 =
5. (3a + 4b – 5c)2 =
6. (5a + 6b – 7c)2 =
7. (8a + 9b – 10c)2 =
8. (2a + 3b – 4c)2 =
9. (10a + 8b – 3c)2 =
10. (8a + 6b – 4c)2 =
13. ( a – b + c )2 = a2 + b2 + c2 – 2ab – 2bc + 2ca
1.(2a – 3b + 4c)2 =
2. (a – 3b + 4c)2 =
3. (2a – b + 4c)2 =
4. (2a – 3b + c)2 =
5. (3a – 4b + 5c)2 =
6. (5a – 6b + 7c)2 =
7. (8a – 9b + 10c)2 =
8. (2a – 3b + 4c)2 =
9. (10a – 8b + 3c)2 =
10. (8a – 6b + 4c)2 =
14. ( a – b – c )2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
1.(2a – 3b – 4c)2 =
2. (a – 3b – 4c)2 =
3. (2a – b – 4c)2 =
4. (2a – 3b – c)2 =
5. (3a – 4b – 5c)2 =
6. (5a – 6b – 7c)2 =
7. (8a – 9b – 10c)2 =
8. (2a – 3b – 4c)2 =
9. (10a – 8b – 3c)2 =
10. (8a – 6b – 4c)2 =
15. ( a + b + c )3 = a3 + b3 + c3 + 3 ( a + b ) ( b + c ) ( c + a )
1.(2a + 3b + 4c)3 =
2. (a + 3b + 4c)3 =
3. (2a + b + 4c)3 =
4. (2a + 3b + c)3 =
5. (3a + 4b + 5c)3 =
6. (5a + 6b + 7c)3 =
7. (8a + 9b + 10c)3 =
8. (2a + 3b + 4c)3 =
9. (10a + 8b + 3c)3 =
10. (8a + 6b + 4c)3 =
16. (a + b – c)3 = a3 + b3 – c3 – 3 (a + b) (b – c) (c – a)
1.(2a + 3b – 4c)3 =
2. (a + 3b – 4c)3 =
3. (2a + b – 4c)3 =
4. (2a + 3b – c)3 =
5. (3a + 4b – 5c)3 =
6. (5a + 6b – 7c)3 =
7. (8a + 9b – 10c)3 =
8. (2a + 3b – 4c)3 =
9. (10a + 8b – 3c)3 =
10. (8a + 6b – 4c)3 =
17. (a – b + c)3 = a3 – b3 + c3 – 3 (a – b) (b – c) (c + a)
1.(2a – 3b + 4c)3 =
2. (a – 3b + 4c)3 =
3. (2a – b + 4c)3 =
4. (2a – 3b + c)3 =
5. (3a – 4b + 5c)3 =
6. (5a – 6b + 7c)3 =
7. (8a – 9b + 10c)3 =
8. (2a – 3b + 4c)3 =
9. (10a – 8b + 3c)3 =
10. (8a – 6b + 4c)3 =
18. (a – b – c)3 = a3 – b3 – c3 + 3 (a – b) (b + c) (c – a)
1.(2a – 3b – 4c)3 =
2. (a – 3b – 4c)3 =
3. (2a – b – 4c)3 =
4. (2a – 3b – c)3 =
5. (3a – 4b – 5c)3 =
6. (5a – 6b – 7c)3 =
7. (8a – 9b – 10c)3 =
8. (2a – 3b – 4c)3 =
9. (10a – 8b – 3c)3 =
10. (8a – 6b – 4c)3 =
19. (a + b)3 = a3 + b3 + 3ab ( a + b )
1. (2a + 3b )3 =
2. (a + 3b )3 =
3. (2a + b )3 =
4. (3a + 4b )3 =
5. (5a + 6b )3 =
6. (8a + 9b )3 =
7. (2a + 5b )3 =
8. (10a + 3b )3 =
9. (12a + 10b )3 =
10. (8a + 10b )3 =
20. (a – b)3 = a3 – b3 – 3ab ( a – b )
1. (2a – 3b )3 =
2. (a – 3b )3 =
3. (2a – b )3 =
4. (3a – 4b )3 =
5. (5a – 6b )3 =
6. (8a – 9b )3 =
7. (2a – 5b )3 =
8. (10a – 3b )3 =
9. (12a – 10b )3 =
10. (8a – 10b )3 =
21. a3 + b3 = (a + b)3 – 3ab (a + b)
= ( a + b ) ( a2 – ab + b2 )
1.(2a)3 + (3b)3 =
2. (3a)3 + (4b)3 =
3. (5a)3 + (4b)3 =
4. (6a)3 + (4b)3 =
5. (8a)3 + (5b)3 =
6. (10a)3 + (5b)3 =
7. (10a)3 + (b)3 =
8. (12a)3 + (10b)3 =
9. (8a)3 + (7b)3 =
10. (a)3 + (3b)3 =
22. a3 – b3 = (a – b)3 + 3ab (a – b)
= ( a – b ) ( a2 + ab + b2 )
1.(2a)3 – (3b)3 =
2. (3a)3 – (4b)3 =
3. (5a)3 – (4b)3 =
4. (6a)3 – (4b)3 =
5. (8a)3 – (5b)3 =
6. (10a)3 – (5b)3 =
7. (10a)3 – (b)3 =
8. (12a)3 – (10b)3 =
9. (8a)3 – (7b)3 =
10. (a)3 – (3b)3 =
23. a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 -ab – bc – ca)
a3 + b3 + c3 – 3abc = 
1.x3 + y3 + z3 – 3xyz =
2. 8x3 + y3 + z3 – 6xyz =
3. x3 + 27y3 + z3 – 9xyz =
4. x3 + y3 + 64z3 – 12xyz =
5. 8x3 + 27y3 + 64z3 – 72xyz =
6. 27x3 + 64y3 + 125z3 – 180xyz =
7. 125a3 + b3 + c3 – 15abc =
8. a3 + b3 + 125c3 – 15abc =
9. a3 + 125b3 + c3 – 15abc =
10. 125a3 + 216b3 + 343c3 – 630abc =
24. a3 – b3 + c3 + 3abc = (a – b + c)(a2 + b2 + c2 + ab + bc – ca)
a3 – b3 + c3 + 3abc = 
1.x3 – y3 + z3 + 3xyz =
2. 8x3 – y3 + z3 + 6xyz =
3. x3 – 27y3 + z3 + 9xyz =
4. x3 – y3 + 64z3 + 12xyz =
5. 8x3 – 27y3 + 64z3 + 72xyz =
6. 27x3 – 64y3 + 125z3 + 180xyz =
7. 125a3 – b3 + c3 + 15abc =
8. a3 – b3 + 125c3 + 15abc =
9. a3 – 125b3 + c3 + 15abc =
10. 125a3 – 216b3 + 343c3 – 630abc =
25. a3 + b3 -c3 +3abc = (a + b – c )(a2 + b2 + c2 – ab + bc + ca)
a3 + b3 – c3 + 3abc = 
1.x3 + y3 – z3 + 3xyz =
2. 8x3 + y3 – z3 + 6xyz =
3. x3 + 27y3 – z3 + 9xyz =
4. x3 + y3 – 64z3 + 12xyz =
5. 8x3 + 27y3 – 64z3 + 72xyz =
6. 27x3 + 64y3 – 125z3 + 180xyz =
7. 125a3 + b3 – c3 + 15abc =
8. a3 + b3 – 125c3 + 15abc =
9. a3 + 125b3 – c3 + 15abc =
10. 125a3 + 216b3 – 343c3 + 630abc =
26. a3 – b3 – c3 – 3abc = (a – b – c )(a2 + b2 + c2 + ab – bc + ca)
a3 – b3 – c3 – 3abc = 
1.x3 – y3 – z3 – 3xyz =
2. 8x3 – y3 – z3 – 6xyz =
3. x3 – 27y3 – z3 – 9xyz =
4. x3 – y3 – 64z3 – 12xyz =
5. 8x3 – 27y3 – 64z3 – 72xyz =
6. 27x3 – 64y3 – 125z3 – 180xyz =
7. 125a3 – b3 – c3 – 15abc =
8. a3 – b3 – 125c3 – 15abc =
9. a3 – 125b3 – c3 – 15abc =
10. 125a3 – 216b3 – 343c3 – 630abc =
27. If a + b + c = 0 then a3 + b3 + c3 = 3abc
28. If a + b + c = 0 then 2(a4 +b4 +c4 ) = (a2 + b2 + c2)2
29. If a + b + c = 0 then (a4 +b4+c4) = 2( a2 b2 + b2 c2 + c2 a2 )2
30. If a = b = c then 3( a2 + b2 + c2 ) = ( a + b + c )2
31. a + b = 
32. a – b = 
33. a4 – b4 = (a + b)(a – b)( a2 + b2 )
1.(2a)4 – (3b)4 =
2. (3a)4 – (4b)4 =
3. (5a)4 – (4b)4 =
4. (6a)4 – (4b)4 =
5. (8a)4 – (5b)4 =
6. (10a)4 – (5b)4 =
7. (10a)4 – (2b)4 =
8. (12a)4 – (10b)4 =
9. (8a)4 – (7b)4 =
10. (9a)4 – (3b)4 =
34. a5 – b5 = ( a – b)( a4 + b4 + a2 b2 + a3 b + a b3 )
1.(2a)5 – (b)5 =
2. (3a)5 – (b)5 =
3. (5a)5 – (4b)5 =
4. (6a)5 – (4b)5 =
5. (8a)5 – (5b)5 =
6. (10a)5 – (5b)5 =
7. (10a)5 – (b)5=
8. (12a)5 – (10b)5 =
9. (8a)5 – (7b)5 =
10. (9a)5 – (3b)5 =
35. a4 + b4 = ( a2 + b2 )2 – 2 a2 b2
a4 + b4 = ( a2 – b2 )2 + 2 a2 b2
1.(2a)4 + (3b)4 =
2. (3a)4 + (4b)4 =
3. (5a)4 + (4b)4 =
4. (6a)4 + (4b)4 =
5. (8a)4 + (5b)4 =
6. (10a)4 + (5b)4 =
7. (10a)4 + (2b)4 =
8. (12a)4 + (10b)4 =
9. (8a)4 + (7b)4 =
10. (9a)4 + (3b)4 =
36. ab = 
= 
1. x . y =
2. y . z =
3. 2a . 3b =
4. 3x . 4y =
5. 5x . 6y =
6. 4a . 5b =
7. 7x . 8y =
8. 10x . 11y =
9. 6x . 5y =
10. 7x . 10y =