Fórmulas álgebra

PREUNIVERSITARIO: INGRESO A LA UNIVERSIDAD
Consulte las páginas Web: www.geocities.com/ingresouniversidad
www.geocities.com/laboticaxx1
José Arturo Barreto, M.A. Universidad de Texas. E-mail: [email protected]
[email protected] [email protected]
[email protected] Tel. (0251)2612905. Barquisimeto. Venezuela
BINOMIO DE NEWTON
n(n − 1) n-2 2 n(n − 1)(n − 2) n-3 3
a b +
a b + … + bn
2
2 x3
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3 (a - b)3 = a3 - 3a2b + 3ab2 – b3
(a + b)n = an + nan-1b +
PRODUCTOS NOTABLES Y FACTORIZACION
a(x + y) = ax + ay
a(x – y) = ax – ay
(x + y) (x – y) = x2 – y2
2
2
3
3
(x + y) (x - xy + y ) = x + y
(x - y) (x2 + xy + y2) = x3 - y3
(x + a) (x + b) = x2 + (a + b) x + ab (ax + b) (cx + d) = acx2 + (ad + bc) x + bd
x 2 + ax + b = ( x + n1 )( x + n 2 ), a = n1 + n 2 , b = n1 n 2
POTENCIACION
(xy)n = xnyn
(xm)nn = xmn
x
xn
  = n
y
 y
x m x n = x m+ n
xm
= x m− n
xn
m
n
x = n xm
1
x −n = n , x ≠ 0
x
1
x −1 = , x ≠ 0
x
−1
x
y
  =
x
 y
0
x =1
0
= 0, si a ≠ 0
a
a
= no definido
0
0
= indeterminado
0
RADICACIÓN
LOGARITMOS
n
a n b = n ab
n
a
=
b
n
a
n
b
m n
a = mn a
n
m
a b=
(a)
n
m
m
mn
n
p
m
a b
= m a np
a =a
n
m
PROGRESIÓN
ARITMÉTICA
Log a x = y ⇔ x = a y
Log a 0 = 1
Log a a = 1
Log a 0 no existe
n
Log (a.b ) = log a. log b
a
Log   = log a - log b
b
log a n = n. Log a
1
log n a = log a
n
TRIGONOMETRIA
( )
a n = a1 + (n − 1)r
 a + an 
sn =  1
.n
 2 
PROGRESIÓN
GEOMÉTRICA
a n = a1 r n −1
sn =
1− rn
.a1
1− r
c1
h
c
Cos α = 2
h
c
Tan α = 1
c2
c
Cot α = 2
c1
h
Sec α =
c2
h
Csc α =
c1
Sen
c1
h
α
c2
α=