what is the formula of algebra
Answers
Answer:
Important Formulas in Algebra
Here is a list of Algebraic formulas –
a2 – b2 = (a – b)(a + b)
(a+b)2 = a2 + 2ab + b2
a2 + b2 = (a + b)2 – 2ab
(a – b)2 = a2 – 2ab + b2
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
(a – b)3 = a3 – 3a2b + 3ab2 – b3
a3 – b3 = (a – b)(a2 + ab + b2)
a3 + b3 = (a + b)(a2 – ab + b2)
(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
(a – b)4 = 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 n is even (n = 2k), an + bn = (a – b)(an-1 + an-2b +…+ bn-2a + bn-1)
If 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
Fractional Exponents a0 = 1 ; aman=am−n ; am = 1a−m ; a−m = 1am
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Answer:
14 formulas
1)a2 – b2 = (a – b)(a + b)
2)(a+b)2 = a2 + 2ab + b2
3)a2 + b2 = (a + b)2 – 2ab
4)(a – b)2 = a2 – 2ab + b2
5)(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
6)(a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
7)(a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
8)(a – b)3 = a3 – 3a2b + 3ab2 – b3
9)a3 – b3 = (a – b)(a2 + ab + b2)
10)a3 + b3 = (a + b)(a2 – ab + b2)
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)