puteri formule matematica

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Formulele inmultirii prescurtate. Puteri 1. (a ± b) 2 = a 2 ± 2ab + b 2 . 2. a 2 - b 2 =(a + b)(a - b). 3. (a ± b) 3 = a 3 ± 3a 2 b +3ab 2 ± b 3 = a 3 ± b 3 ± 3ab(a ± b). 4. a 3 ± b 3 =(a ± b)(a 2 ab + b 2 ). 5. (a 1 a 2 ...a m ) n = a n 1 a n 2 ...a n m m, n N,a i 0,i = 1,n. 6. a n 1 a n 2 ...a n m = a n 1 +n 2 +...+n m m, n N,a 0. 7. a m a n = a m-n m, n N,a> 0. 8. (a m ) n = a m·n m, n N,a> 0. 9. a -n = 1 a n n N,a> 0. 10. a m n = n a m m, n N,n 2. 11. n a m = a m n , daca m =2k +1 |a| m n , daca m =2k k, m, n N,n 2. 12. ( n a) m = n a m m, n N,n 2. 13. n a 1 a 2 ...a m = n q |a 1 | n q |a 2 | ... n q |a m | m, n N,n 2. 14. n r a b = n q |a| n q |b| (b 6= 0). ( n a + b 6= n a + n b, a 6=0,b 6= 0). n N,n 2. 0 Copyright c 1999 ONG TCV Scoala Virtuala a Tanarului Matematician http://math.ournet.md 1

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Puteri formule matematica

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Page 1: Puteri formule matematica

Formulele inmultirii prescurtate. Puteri

1. (a± b)2 = a2 ± 2ab+ b2.

2. a2 − b2 = (a+ b)(a− b).

3. (a± b)3 = a3 ± 3a2b+ 3ab2 ± b3 = a3 ± b3 ± 3ab(a± b).

4. a3 ± b3 = (a± b)(a2 ∓ ab+ b2).

5. (a1a2 . . . am)n = an1an2 . . . a

nm m,n ∈ N, ai ≥ 0, i = 1, n.

6. an1an2 . . . anm = an1+n2+...+nm m,n ∈ N, a ≥ 0.

7.am

an= am−n m,n ∈ N, a > 0.

8. (am)n = am·n m,n ∈ N, a > 0.

9. a−n =1an

n ∈ N, a > 0.

10. amn = n

√am m,n ∈ N, n ≥ 2.

11. n√am =

amn , daca m = 2k + 1

|a|mn , daca m = 2kk,m, n ∈ N, n ≥ 2.

12. ( n√a)m = n

√am m,n ∈ N, n ≥ 2.

13. n√a1a2 . . . am = n

√|a1| n

√|a2| . . . n

√|am| m,n ∈ N, n ≥ 2.

14. n

√a

b=

n

√|a|

n

√|b|

(b 6= 0). ( n√a+ b 6= n

√a+ n√b, a 6= 0, b 6= 0). n ∈ N, n ≥ 2.

0 Copyright c©1999 ONG TCV Scoala Virtuala a Tanarului Matematician http://math.ournet.md

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