Hello friends, in this post I have told about the formula related to algebra, hope you will like this post.
⇜Very Important Formulas in Algebra⇝
Below is the list of Algebraic formulas๐
· (a + b)2 =(a + b) (a + b)= a2 + 2ab + b2
· a2 – b2 = (a – b) (a + b)
· a2 + b2 = (a + b)2 – 2ab
· (a – b)2 = (a - b) (a - b)=a2 – 2ab + b2
· (a + b + c)2 =(a + b + c) (a + b + c)= a2 + b2 + c2 + 2ab + 2bc + 2ca
· (a – b – c)2 =(a - b - c) (a - b - c)= a2 + b2 + c2 – 2ab + 2bc – 2ca
· (a + b)3 =(a + b) (a + b) (a + b)= a3 + 3a2b + 3ab2 + b3
· (a + b)3 = a3 + b3 + 3ab(a + b)
· (a – b)3 =(a – b) (a – b) (a – b)= a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
· a3 – b3 = (a – b) (a2 + ab + b2)
· a3 + b3 = (a + b) (a2 – ab + b2)
· (a + b)4 =(a + b) (a + b) (a + b) (a + b) = a4 + 4a3b + 6a2b2 + 4ab3 + b4
· (a – b)4 =(a – b) (a – b) (a – b) (a – b) = a4 – 4a3b + 6a2b2 – 4ab3 + b4
· a4 – b4 = (a – b) (a + b) (a2 + b2)
· a5 – b5 = (a – b) (a4 + a3b + a2b2 + ab3 + b4)
If n is a natural number an – bn = (a – b) (an-1 + an-2b+…+ bn-2a + bn-1)
If natural number n is even (n = 2k), an + bn = (a + b) (an-1 – an-2b +…+ bn-2a – bn-1)
If natural number n is odd (n = 2k + 1), an + bn = (a + b) (an-1 – an-2b +an-3b2…- bn-2a + bn-1)
(a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)
Laws of Exponents
· (am) (an) = am+n
· (ab)m = ambm
· (am)n = amn
Factorials
· n! = (1).(2).(3)…..(n − 1).n
· n! = n(n − 1)! = n(n − 1)(n − 2)! = ….
· 0! = 1
