2.-

4.- (x+y)2 - x(x-y)2

y xy

m.c.m.

[x(x+2)2] x(x-y)2

xy xy

= x(x+y)2 - x(x-y)2

xy

= x3+2x2y+xy2-x3+2x2y-xy2

xy

= 4x2y

xy

6._ a + 1+5a = a3-5a+1+5a = a3+1 = (a+1)(a2-a+1)

a2-5 a2-5 a2-5 a2-5

a – a+5 = a2+a-a-5 = a2-5

a+1 a+1 a+1

(a+1)(a2-a+1) . a2-5 = a2-a+1

a2-5 a+1

N# 8

10._ x3-xy2 = x2+xy

x-y

x3-xy2 = x(x+y)

x-y

x (x2-y2) = x(x+y)

x-y

x(x+y)(x-y) = x (x+y)

x-y

x (x+y) = x (x+y)

12.-

Ejercicio 14

a2 - a4 x 1-a + 1+ a3 m.c.m: (a-1) (a+1) (a-1) (a+1)=(a2+1)(a2-1)

1-a2 1-a4 a2. a2-1: (a-1) (a+1)

a4-1: (a2-1) (a2+1)=

(a-1) (a+1)(a-1) (a+1)

a2 (a2-1) - (a2)(a2) X 1-a + 1-a3.

(a2+1)(a2-1) a2.

a4- a4-a2. X (1-a)(a2) + a3+1

(a2+1)(a2-1) a2

a2. X a2-a3 + a3 +1

(a4-1) a2

a2 X a2+1

(a2+1)(a2-1) a2

(a2 ) ( a2+1)

(a2+1)(a2-1) (a2)

R=a2-1

N# 16

Factorización de:

Factorización de:

Ejercicio 18

1 - 2 + 3 ÷ x + x + 6

x x+2 x+3 x+2 x+3 x2+5x+6

(1)(x+2)(x+3) - [(2)(x)(x+3)] +(3)(x)(x+2) 6 ÷ (x)(x+3) + (x)(x+2) + 6

(x ) ( x+2) ( x+3) (x+2) (x+3)

x2+5x+6 – 2x2-6x-6 + 3x2+6x ÷ x2+3x + x2+2x + 6

(x ) ( x+2) ( x+3) (x+2) (x+3)

2x2+5x+6 ÷ 2x2+5x+6

(x ) ( x+2) ( x+3) (x+2) (x+3)

(2x2+5x+6)(x+2) (x+3) m.c.m (x+2)(x+3)

(x ) ( x+2) ( x+3) (2x2+5x+6) x+2 = x+2

x+3= x+3

(x+2) (x+3) (x+2) (x+3) x2+5x+6=

(x+2) (x+3) (x ) ( x+2) ( x+3) (x+2)(x+3)

R= 1

X

20._ 1 x2-36 ÷ x . 1 . 1 _

3 x x2-4 x-36 x-4x

x x

m.c.m

x2-36 = (x+6) (x-6)

x2-4 = (x+2) (x-2)

1 (x+6) (x-6) ÷ x . 1 . 1 _

3 x (x+2) (x-2) x-36 x-4x

x x

(x+6) (x-6) . (x+2) (x-2) . x . x__

3x x x2-36 x2-4x

x2 (x+6) (x-6) (x+2) (x-2) = x2 = 1

3x2 (x+6) (x-6) (x+2) (x-2) 3x2 3

22.-

.

.

24.-

. a-b

.

1

=

—

a-b