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Important algebraic formula for all students

Some important algebraic formula





1.     a² + b² = (a+b)² -2ab

        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
      
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