Explicație pas cu pas:
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 + 3ab2 ± b
3 = a
3 ± b
3 ± 3ab(a ± b).
4. a
3 ± b
3 = (a ± b)(a
2 ∓ ab + b
2
).
5. (a1a2 . . . am)
n = a
n
1 a
n
2
. . . an
m m, n ∈ N, ai ≥ 0, i = 1, n.
6. a
n1 a
n2
. . . anm = a
n1+n2+...+nm 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
am m, n ∈ N, n ≥ 2.
11. √n
am =
a
m
n , daca m = 2k + 1
|a|
m
n , daca m = 2k
k, m, n ∈ N, n ≥ 2.
12. (
√n a)
m =
√n
am m, n ∈ N, n ≥ 2.
13. √n a1a2 . . . am = n
q
|a1|
n
q
|a2| . . .
n
q
|am| m, n ∈ N, n ≥ 2.
14. n
ra
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.
