Some important algebraic formula
a² + b² = (a-b)² +2ab
2. a² – b² = (a-b)(a+b)
3. (a+b)² = a² + 2ab + b²
4. (a-b)² = a² – 2ab + b²
5. (a+b+c)² = a²+b²+c²+2ab+2ac+2bc
6. (a-b-c)² = a²+b²+c²-2ab-2ac+2bc
7. a³-b³ = (a-b) (a² + ab + b²)
8. a³+b³ = (a+b) (a² – ab + b²)
9. (a+b)³ = a³+ 3a²b + 3ab² + b³
10. (a-b)³ = a³- 3a²b + 3ab² – b³
11. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
12. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 +b⁴
13. a4 – b4 = (a – b)(a + b)(a2 + b2)
14. a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
15.a³ + b³ + c³ -3abc = ( a + b + c)(a² + b² + c² - ab - bc - ca)
16. ab =(a+b/2)² - (a-b/2)²
17. (a+b)² - (a-b)² = 4ab
18. If a+b+c =0 then,
a³ + b³ + c³ = 3abc