Algebra Formulas List
1. (a + b)2 = a2 + b2 + 2ab
2. (a – b)2 = a2 + b2 – 2ab
3. a2 – b2 = (a + b) (a – b)
4. a2 + b2 = (a + b)2 – 2ab or a2 + b2 = (a – b)2 + 2ab
5. a3 + b3 = (a + b) (a2 – ab + b2) = (a + b)3 – 3ab(a + b)
6. a3 – b3 = (a – b) (a2 + ab + b2) = (a – b)3 + 3ab(a – b)
7. 2(a2 + b2) = (a+ b)2 + (a – b)2
8. (a + b)2 – (a – b)2 = 4ab
9. a4 + b4 = (a + b) (a – b) [(a + b)2 – 2ab)]
10. (a – b)2 = (a + b)2 – 4ab
11. (a + b)2 = (a – b)2 + 4ab
12. a4 + b4 = [(a + b)2 – 2ab]2 – 2(ab)2
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)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
16. a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
17. a4 + a2b2 + b4 = (a2 + ab + b2) (a2 – ab + b2)
18. a4 + a2 + 1 = (a2 + a + 1) (a2 – a + 1)
19. if a + b + c = 0 then a3 + b3 + c3 = 3abc
20. a8 – b8 = (a4 + b4) (a2 + b2) (a + b) (a – b)
Absolutely! Let's break down those algebraic formulas with examples and then convert them
into word form.
Formula Examples:
1. (a + b)² = a² + b² + 2ab
o Example: (3 + 4)² = 3² + 4² + 2(3)(4)
49 = 9 + 16 + 24
49 = 49
2. (a – b)² = a² + b² – 2ab
o Example: (5 – 2)² = 5² + 2² – 2(5)(2)
9 = 25 + 4 – 20
9=9
, 3. a² – b² = (a + b)(a – b)
o Example: 7² – 3² = (7 + 3)(7 – 3)
49 – 9 = (10)(4)
40 = 40
4. a² + b² = (a + b)² – 2ab or a² + b² = (a – b)² + 2ab
o Example: 4² + 5² = (4 + 5)² – 2(4)(5)
16 + 25 = 81 – 40
41 = 41
o Example: 4² + 5² = (4-5)² + 2(4)(5)
16+25 = 1 + 40
41 = 41
5. a³ + b³ = (a + b)(a² – ab + b²) = (a + b)³ – 3ab(a + b)
o Example: 2³ + 3³ = (2 + 3)(2² – 2(3) + 3²)
8 + 27 = (5)(4 – 6 + 9)
35 = (5)(7)
35 = 35
o Example: 2³ + 3³ = (2+3)³ - 3(2)(3)(2+3)
8+27 = 125 - 18(5)
35 = 125-90
35 = 35
6. a³ – b³ = (a – b)(a² + ab + b²) = (a – b)³ + 3ab(a – b)
o Example: 5³ – 2³ = (5 – 2)(5² + 5(2) + 2²)
125 – 8 = (3)(25 + 10 + 4)
117 = (3)(39)
117 = 117
o Example: 5³ - 2³ = (5-2)³ + 3(5)(2)(5-2)
125-8 = 27 + 30(3)
117 = 27+90
117 = 117
1. (a + b)2 = a2 + b2 + 2ab
2. (a – b)2 = a2 + b2 – 2ab
3. a2 – b2 = (a + b) (a – b)
4. a2 + b2 = (a + b)2 – 2ab or a2 + b2 = (a – b)2 + 2ab
5. a3 + b3 = (a + b) (a2 – ab + b2) = (a + b)3 – 3ab(a + b)
6. a3 – b3 = (a – b) (a2 + ab + b2) = (a – b)3 + 3ab(a – b)
7. 2(a2 + b2) = (a+ b)2 + (a – b)2
8. (a + b)2 – (a – b)2 = 4ab
9. a4 + b4 = (a + b) (a – b) [(a + b)2 – 2ab)]
10. (a – b)2 = (a + b)2 – 4ab
11. (a + b)2 = (a – b)2 + 4ab
12. a4 + b4 = [(a + b)2 – 2ab]2 – 2(ab)2
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)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
16. a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2 – ab – bc – ca)
17. a4 + a2b2 + b4 = (a2 + ab + b2) (a2 – ab + b2)
18. a4 + a2 + 1 = (a2 + a + 1) (a2 – a + 1)
19. if a + b + c = 0 then a3 + b3 + c3 = 3abc
20. a8 – b8 = (a4 + b4) (a2 + b2) (a + b) (a – b)
Absolutely! Let's break down those algebraic formulas with examples and then convert them
into word form.
Formula Examples:
1. (a + b)² = a² + b² + 2ab
o Example: (3 + 4)² = 3² + 4² + 2(3)(4)
49 = 9 + 16 + 24
49 = 49
2. (a – b)² = a² + b² – 2ab
o Example: (5 – 2)² = 5² + 2² – 2(5)(2)
9 = 25 + 4 – 20
9=9
, 3. a² – b² = (a + b)(a – b)
o Example: 7² – 3² = (7 + 3)(7 – 3)
49 – 9 = (10)(4)
40 = 40
4. a² + b² = (a + b)² – 2ab or a² + b² = (a – b)² + 2ab
o Example: 4² + 5² = (4 + 5)² – 2(4)(5)
16 + 25 = 81 – 40
41 = 41
o Example: 4² + 5² = (4-5)² + 2(4)(5)
16+25 = 1 + 40
41 = 41
5. a³ + b³ = (a + b)(a² – ab + b²) = (a + b)³ – 3ab(a + b)
o Example: 2³ + 3³ = (2 + 3)(2² – 2(3) + 3²)
8 + 27 = (5)(4 – 6 + 9)
35 = (5)(7)
35 = 35
o Example: 2³ + 3³ = (2+3)³ - 3(2)(3)(2+3)
8+27 = 125 - 18(5)
35 = 125-90
35 = 35
6. a³ – b³ = (a – b)(a² + ab + b²) = (a – b)³ + 3ab(a – b)
o Example: 5³ – 2³ = (5 – 2)(5² + 5(2) + 2²)
125 – 8 = (3)(25 + 10 + 4)
117 = (3)(39)
117 = 117
o Example: 5³ - 2³ = (5-2)³ + 3(5)(2)(5-2)
125-8 = 27 + 30(3)
117 = 27+90
117 = 117
