Ley absorbente del cero y neutralidad del 1

a · 0 = 0 1 · a = a

Distribuciones

− (a± b) = −a∓ b a (b + c) = ab + ac

a (b + c) (d + e) = abd + abe + acd + ace (a + b) (c + d) = ac + ad + bc + bd

− (−a) = a

Inversos multiplicativos...Fracciones

0

a= 0, a 6= 0

a

1= a

a

a= 1

(ab

)−1=

1ab

=b

a(ab

)−c=

((ab

)−1)c

=

(b

a

)c −a−b

=a

b

a−b =1

ab−a−b

=a

b−ab

= −a

b

a

−b= −a

b

−ab

= −a

b

bc

a=

b

c · a1bc

=c

b

Valor Absoluto

|−a| = a |a| = a , a ≥ 0

|−a| = |a| |ax| = a |x| , a ≥ 0

Reglas de Exponentes

1a = 1 a1 = a

a0 = 1 , a 6= 0 0a = 0 , a 6= 0

(ab)n = anbnam

an= am−n , m > n(

ab)c

= ab·c(ab)c

= ab·c(ab

)c=

ac

bca

mn =

(n√a)m

ac · bc = (a · b)c n√a · b = n

√a

n√b

1

Formulas Notables

x2 − y2 = (x− y) (x + y)

x3 + y3 = (x + y)(x2 − xy + y2

)4

xn − yn = (x− y)(xn−1 + xn−2y + · · ·+ xyn−2 + yn−1

)xn + yn = (x + y)

(xn−1 − xn−2y + · · · − xyn−2 + yn−1

)ax(2n) − b =

(√axn +

√b)(√

axn −√b)

ax4 − b =(√

ax2 +√b)(√

ax2 −√b)

ax(2n) − by(2m) =(√

axn +√bym

)(√axn −

√bym

)ax4 − by4 =

(√ax2 +

√by2

)(√ax2 −

√by2

)Reglas Logarítmicas

log (0) = −∞ log (1) = 0

loga (a) = 1 loga

(xb)

= b · loga (x)

logab (x) =1

bloga (x) loga

(1

x

)= − loga (x)

log 1a

(x) = − loga (x) logxn (x) =1

n

loga (b) =ln (b)

ln (a)logx (xn) = n

logx

((1

x

)n)= −n aloga(b) = b

In-de�niciones

00 = indefinidox

0= indefinido

loga (b) = indefinido , a < 0 loga (b) = indefinido , b < 0

log1 (a) = indefinido log0 (a) = indefinido

Números que no pertenecen a R

i2 = −1√−1 = i

√−a =

√−1√a

2