0000555122 Productos Notables

1

5 GRADO DE PRIMARIA 2 012

Prof: Wilfredo F. Cuellar Casa I. E. P. T R I L C E

CUADRADO DE UN BINOMIO:

E J E R C I C I O S

( x + 4 )2 = ( x )

2 + 2 ( x )( 4 ) + ( 4 )

2

= x2 + 8x + 16

( 4a - 3 )2 = ( 4a )

2 - 2 ( 4a )( 3 ) + ( 3 )

2

= 16 a2 - 24 a + 9

( 3 y4 + 5 )

2 = ( 3 y

4 )

2 + 2 ( 3 y )( 5 ) + ( 5 )

2

= 9 y8 + 30 y + 25

( a + b )2 = ( a )

2 + 2 ( a )( b ) + ( b )

3

( a - b )2 = ( a )

2 - 2 ( a )( b ) + ( b )

3

Se denominan productos notables a ciertas

multiplicaciones que presentan una forma

pecualiar, evitando la operacin de la

multiplicacin, y escribiendo en forma

directa el resultado.

2



PRACTICAMOS

2( 5)x ______________________________________________________________________________

______________________________________________________________________________

2(3 4)x _____________________________________________________________________________

______________________________________________________________________________

4 2( 6)x _____________________________________________________________________________

______________________________________________________________________________

2 2(5 2)a ____________________________________________________________________________

______________________________________________________________________________

2 2(4 3 )m a __________________________________________________________________________

______________________________________________________________________________

3 4 2(5 2 )a m ________________________________________________________________________

______________________________________________________________________________

2 2(4 3 )m a __________________________________________________________________________

______________________________________________________________________________

3



Nivel I

01 Resolver: 2 2

( 3) 6x x x

a) 6 b) 9 c) 12 d) 12x e) 3x 02 Resolver:

2 2( 7) 49x x

a) 98 b) 14 c) 28 d) 14x e) 49x 03 Resolver:

2 2 2( 4) ( 8) 2 80a a a

a) 24a b) 16a c) 160 d) 56 e) 40 04 Reducir:

2 2 2( 1) ( 5) 2 12 6m m m m

a) 20m b) 29m c) 43 d) 20 e) 32 05 Reducir:

2 2 2( 9) ( 4) 2 17y y y

a) 26y - 82 b) 26y + 82 c) 25y + 80 d) 24y + 84 e) 26y + 80 06 Reducir:

2 2 2( 3) ( 10) 26 2c c c c

a) 107 b) 108 c) 101 d) 103 e) 109 07 Reducir:

2 2 2(3 2) (5 1) 34 5x x x

a) 21x b) 10 c) 29x d) 12x e) 22x

08 Resolver:

2 2 2(4 3) (6 5) 34 84 5x x x x

a) 81x2 b) 19x2 c) 29x2

d) 57x2 e) 50x2

09 Resolver:

2 2 2(2 7) (3 1) 50 6 13x x x x

a) 24x b) 38x c) 42x d) 21x e) 40x 10 Reducir:

2 2 2(3 4) (2 3) 25 36 7x x x x

a) 18x2 b) 19x2 c) 20x2

d) 21x2 e) 22x2

11 Reducir:

2 2 2 2(2 5) (3 4) (4 3) 68 29x x x x x

a) 25 b) 16 c) 9 d) 50 e) 41 12 Reducir:

2 2 2 2(3 1) (5 3) (7 5) 6 106 83x x x x x

a) 29 b) 41 c) 36 d) 18 e) 20 13 Reducir:

2 2 2( 12) ( 1) 145 2x x x

a) 16x b) 26x c) 19x d) 33x e) 25x 14 Efectuar:

2(3 2 2 6) 24 3

a) 45 b) 44 c) 43 d) 42 e) 41

4



Nivel II

01 Reducir: 2

( 2) ( 4)x x x

a) 10 b) 5 c) 4 d) 3 e) 12 02 Resolver:

2 2 2(2 5) ( 3) 26 5x x x x

a) 31 b) 32 c) 33 d) 34 e) 35 03 Reducir:

2( 3 6) 9 3 2

a) 5 2 b) 2 2 c) 8 2 d) 9 2 e) 4 2

04 Efectuar:

2 2( 3 8) ( 12 2) 25 10 6

a) 8 6 b) 6 6 c) 8 2 d) 12 6 e)18 6

05 Resolver:

2 2( 3 12) ( 5 10) 10 2

a) 39 b) 40 c) 41 d) 42 e) 43 06 Resolver:

2 2( 2 14) ( 6 8) 8 3 4 7

a) 25 b) 36 c) 51 d) 21 e) 30 07 Reducir:

2(3 5 5 2) 30 10

a) 42 b) 72 c) 37 d) 95 e) 106

08 Resolver:

2 2 2(2 3) ( 6) 15 5x x x

a) 19 b) 29 c) 30 d) 39 e) 32 09 Reducir:

2 2 2( 8) (2 4) 80 9x x x

a) 14x2 b) 16x2 c) 13x2

d) 20x2 e) 15x2

10 Reducir:

2 2 2(5 3) (3 1) 10 34x x x


2 2(2 3 3 5) (4 2 3 3) 24 6 12 15

a) 105 b) 106 c) 111 d) 116 e) 134 12 Hallar:

2 2 2(4 1) ( 2) 2(6 ) 17R x x x x

a) 2 b) 3 c) 4 d) 5 e) 6 13 Calcular:

2 2 2(5 2) (2 5) 29F x x x

a) 28 b) 29 c) 30 d) 31 e) 32 14 Calcular:

2 2( 5) (3 1) 2 (5 8 )W x x x x x

a) 24 b) 25 c) 26 d) 27 e) 28

5



IDENTIDAD DE LEGENDRE:

E J E R C I C I O S

( x + 4 )2 - ( x - 4 )

2 = 4 ( x )( 4 )

= 16 x

( 4a + 3 )2 + ( 4a - 3 )

2 = 2 [( 4a )2 + ( 3 )2 ]

= 2 [16 a2 + 9 ]

= 32 a2 + 18

( 3 y4 + 5 )

2 + ( 3 y

4 - 5 )

2 = 2 [( 3 y4 )2 + ( 5 )2 ]

= 2 [ 9 y8 + 25 ]

= 18 y8 + 50

( a + b )2 - ( a - b )

2 = 4( a )( b )

( a + b )2 + ( a - b )

2 = 2 [a2 + b2 ]

6



PRACTICAMOS

2 2( 5) ( 5)x x ______________________________________________________________________

_______________________________________________________________________

2 2(3 4) (3 4)x x ___________________________________________________________________

_______________________________________________________________________

4 2 4 2( 6) ( 6)x x ___________________________________________________________________

________________________________________________________________________

2 2 2 2(5 2) (5 2)a a ________________________________________________________________

______________________________________________________________________

2 2 2 2(4 3 ) (4 3 )m a m a ___________________________________________________________

___________________________________________________________________

3 4 2 3 4 2(5 2 ) (5 2 )a m a m _________________________________________________________

___________________________________________________________________

2 2 2 2(4 3 ) (4 3 )m a m a ___________________________________________________________

__________________________________________________________________

7



Nivel I

01 Resolver: 2 2

( 3) ( 3)x x

a) 6x b) 8x c) 10x d) 12x e) 14x 02 Resolver:

2 2(2 3) (2 3)y y

a) 24y b) 18y c) 20y d) 13y e) 28y 03 Resolver:

2 2(3 5 ) (3 5 ) 42b a b a ab

a) 16ab b) 9ab c) 26ab d) 18ab e) 28ab 04 Resolver:

2 2(7 ) (7 ) 9x y x y yx

a) 36xy b) 37xy c) 11yx d) 7xy e) 4xy 05 Resolver:

2 2(2 3) (2 3)ax ax ax

a) 25ax b) 17ax c) 19ax d) 5ax e) 9ax 06 Resolver:

2 2( 8) ( 8) 15m m m

a) 15m b) 16m c) 17m d) 18m e) 19m 07 Resolver:

2 2(5 2 ) (5 2 ) 25a b a b ab

a) 16ab b) 15ab c) 14ab d) 13ab e) 12ab

08 Resolver:

2 2 2(2 5) (2 5) 8y y y

a) 25 b) 35 c) 15 d) 50 e) 100 09 Resolver:

2 2 2(3 2) (3 2) 18b b b

a) 10 b) 8 c) 12 d) 6 e) 14 10 Resolver:

2 2 2(4 2) (4 2) 32x x x

a) 6 b) 14 c) 10 d) 8 e) 12 11 Resolver:

2 2 2 2( 3) ( 3) 2ay ay a y

a) 20 b) 12 c) 18 d) 6 e) 10 12 Resolver:

2 2(2 5) (2 5) 50a a

a) 4a2 b) 16a2 c) 2a2 d) 8a2 e) 100

13 Resolver:

2 2 2(2 5 ) (2 5 ) 8a b a b a

a) 25b2 b) 100b2 c) 50b2 d) 15b2 e) 10b2

14 Resolver:

2 2

2 2 3 3 2 2 3 3

a) 74 b) 52 c) 71 d) 80 e) 70

8



Nivel II

01 Resolver: 2 2 2

( 1) ( 1) 2x x x

a) 4 b) 2 c) 1 d) 8 e) 12 02 Resolver:

2 2

2 8 + 2 + 2 8 - 2 - 15

a) 54 b) 53 c) 52 d) 51 e) 50 03 Resolver:

2 2

2 5 + 10 + 2 5 - 10 - 54

a) 3 b) 4 c) 5 d) 6 e) 7 04 Resolver:

2 2

5 + 2 3 + 5 - 2 3 - 31

a) 1 b) 2 c) 3 d) 4 e) 5 05 Resolver:

2 2

8 + 2 5 + 8 - 2 5 - 10

a) 46 b) 50 c) 41 d) 41 e) 52 06 Resolver:

2 2

6 2 + 3 + 6 2 - 3 - 90

a) 76 b) 60 c) 84 d) 91 e) 29 07 Resolver:

2 22 5 2 5 38x x x

a) x b) x2 c) 2x2 d) 2x e) 5x

08 Resolver:

2 2

3 6 2 3 3 6 2 3 28 2

a) 44 2 b) 36 2 c) 48 2 d) 22 2 e)12 2

09 Resolver:

2 2

5 8 + 2 2 - 5 8 - 2 2

a) 160 b) 150 c) 140 d) 130 e) 120 10 Resolver:

2 2

6 5 + 10 - 6 5 - 10 - 94 2

a) 5 2 b) 6 2 c) 7 2 d) 8 2 e) 9 2

11 Resolver:

2 2

6 + 4 8 - 6 - 4 8 - 63 3

a) 2 3 b) 6 3 c) 9 3 d) 10 3 e) 3

12 Resolver:

2 2

3 3 32 5 2 5 13x x x

a) 51x3 b) 55x3 c) 53x3 d) 58x3 e) 60x3

13 Resolver:

2 2

4 4 47 3 7 3 75x x x

a) 9x4 b) 12x4 c) 8x4 d) 4x4 e) 11x4

14 Resolver:

2 2

2 + 4 3 + 2 - 4 3 - 68

a) 29 b) 30 c) 31 d) 32 e) 33

9



CUBO DE UN BINOMIO:

E J E R C I C I O S

( x + 3 )3 = ( x )

3 + ( 3 )

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

= x3 + 27 + 9 x ( x + 3 )

= x3 + 27 + 9 x

2 + 27 x

( 4a - 2 )3 = ( 4a )

3 - ( 2 )

3 - 3( 4a )( 2 )( 4a - 2 )

= 64 a3 - 8 - 24 a ( 4a - 2 )

= 64 a3 - 8 - 96 a

2 + 48 a

( 5 m4 + 2 )

3 = ( 5m

4 )

3 + ( 2 )

3 + 3( 5m

4 )( 2 )( 5m

4 + 2 )

= 125 m12

+ 8 + 30 m4 ( 5m

4 + 2 )

= 125 m12

+ 8 + 150 m8 + 60 m

4

( a + b )3 = ( a )

3 + ( b )

3 + 3( a )( b )( a + b )

( a - b )3 = ( a )

3 - ( b )

3 - 3( a )( b )( a - b )

10



PRACTICAMOS

3( 5)x ____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

3(3 2)x ___________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

2 3( 5)x ___________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

5 3(3 4)a __________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

2 3(3 2 )m a ________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

4 3 3(2 3 )a m ______________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

11



3(2 1)x ___________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

3(4 3 )x ___________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

3 3(2 1)x __________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

2 3(4 3)y __________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

9 3(2 4 )a b ________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

3 4 3( 5 )a b ______________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

12



Nivel I 01 Si: a + b = 3 ab = 4 Calcular: a3 + b3

a) 45 b) 18 c) - 9 d) 40 e) - 12 02 Si: a + b = 2 ab = 3 Calcular: a3 + b3

a) 12 b) 11 c) - 15 d) 16 e) - 10 03 Si: a + b = 5 ab = 12 Calcular: a3 + b3

a) 116 b) 46 c) - 120 d) - 55 e) 42 04 Si: a - b = 6 ab = 20 Calcular: a3 - b3

a) 146 b) - 144 c) - 146 d) - 139 e) 148 05 Si: a - b = 3 ab = - 5 Calcular: a3 - b3

a) 12 b) - 10 c) - 18 d) - 8 e) 17 06 Si: a + b = 3 ab = 3 Calcular: a3 + b3

a) 18 b) - 8 c) - 6 d) 0 e) 14 07 Si: a + b = 6 ab = 10 Calcular: a3 + b3

a) 24 b) - 34 c) 36 d) - 44 e) 46 08 Si: a - b = 4 ab = - 7 Calcular: a3 - b3

a) 14 b) 18 c) - 20 d) - 28 e) 32 09 Si: a + b = 2 ab = 1 Calcular: a3 + b3

a) 3 b) 4 c) 5 d) 6 e) 2 10 Si: a - b = 6 ab = - 1 Calcular: a3 - b3

a) 194 b) 192 c) 198 d) 198 e) 191 11 Si: a + b = 4 ab = 7 Calcular: a3 + b3

a) 100 b) 81 c) - 20 d) - 92 e) 96 12 Si: a - b = 5 ab = - 10

Calcular: a3 - b3

a) 15 b) - 5 c) - 55 d) - 25 e) 125 13 Si: a + b = 6 ab = 12 Calcular: a3 + b3

a) 12 b) 4 c) - 1 d) 0 e) 2

13



PRODUCTO DE DOS FACTORES CON UN TRMINO COMN:

E J E R C I C I O S

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

= x2 + 8 x + 15

( a + 2 ) ( a + 5 ) = ( a )2 + ( 2 + 5 )( a ) + ( 2 )( 5 )

= a2 + 7 a + 10

( 5 m - 3 ) ( 5 m + 6 ) = ( 5m )2 + ( - 3 + 6 )( 5m ) + ( - 3 )( 6 )

= 25 m2 + ( 3 )( 5m ) + ( - 18 )

= 25 m2 + 15 m - 18

( 3y - 4 ) ( 3y - 7 ) = ( 3y )2 + ( - 4 - 7 )( 3y ) + ( - 4 )( - 7 )

= 9 y2 + ( - 11)( 3y ) + ( 28 )

= 9 y2 - 33 y + 28

( x + a ) ( x + b ) = ( x )2 + ( a + b )( x ) + ( a )( b )

14



( 8)( 3)x x

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( 2)( 5)x x

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( 3)( 1)x x

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( 4)( 1)a a

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( 2)( 5)m m

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( 3)( 9)a a

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( 4)( 9)x x

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( 2)( 7)x x

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( 8)( 9)x x

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( 5)( 8)x x

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( 3)( 11)x x

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( 7)( 8)x x

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( 5)( 9)x x

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( 4)( 6)x x

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( 2)( 5)a a

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( 9)( 4)a a

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( 3)( 11)a a

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( 6)( 7)a a

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( 8)( 9)x x

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( 2)( 13)x x

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( 5)( 12)x x

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( 5)( 10)x x

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( 8)( 14)x x

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( 5)( 13)m m

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16



01 Resolver:

2( 2)( 5) 7m m m m

a) 7 b) 3 c) 25 d) 10 e) 52 02 Reducir:

2( 3)( 6) 18x x x


( 4)( 8) ( 12)x x x x

a) 18 b) 32 c) 12 d) 4 e) 20 04 Calcular:

( 1)( 8) ( 3)( 6) 2 ( 9) 2A x x x x x x

a) 14 b) 18 c) 24 d) 29 e) 32 05 Calcular:

2( 2)( 6) ( 5)( 3) 2 27R x x x x x

a) 16x b) 10x c) 14x d) 8x e) 12x 06 Calcular:

( 7)( 3) ( 6)( 4) 2 ( 10)M x x x x x x

a) 19 b) 20 c) 21 d) 24 e) 45

07 Si: 2

7 4x x Hallar:

H = ( x + 2 )( x + 5 ) + ( x + 3 )( x + 4 )

a) 14 b) 30 c) 24 d) 18 e) 25

08 Calcular:

2( 5)( 7) ( 9)( 3) 2 8F x x x x x

a) - 47 b) 70 c) 80 d) - 60 e) 50 09 Calcular:

2( 5)( 2) ( 1)( 3) 2 9S x x x x x

a) - 11 b) 17 c) 16 d) - 3 e) 11 10 Calcular:

2(2 7)(2 1) (3 1)(3 3) 5 4T x x x x x

a) 18x2 b) 12x2 c) 8x2 d) 7x2 e) 9x2

11 Calcular:

2( 6)( 9) ( 4)( 1) 2P x x x x x

a) - 50 b) 50 c) 48 d) - 58 e) 57

12 Se sabe que: 2

10 15x x Hallar:

( 4)( 6)

( 2)( 8)

x x

x x

a) 9 b) 19 c) 3 d) 27 e) 18

13 Sabiendo que: 2

6 3x x

Hallar:

( 5)( 1)( 2)( 4)T x x x x

a) 7 b) 8 c) 9 d) 10 e) 11

14 Sabiendo que: 2

5 6x x

Hallar:

( 3)( 2) ( 1)( 4)A x x x x

a) - 8 b) 10 c) 12 d) - 2 e) 4

17



15 Calcular:

( 4)( 7) ( 2)( 9) 2 ( 11)C x x x x x x

a) 44 b) 38 c) 48 d) 28 e) 46

16 Si: 2

9 12 0x x

Calcular:

( 7)( 2) ( 5)( 4) 8M x x x x

a) 2 b) 18 c) 10 d) - 10 e) 14

17 Siendo: 2

11 20 0x x

Calcular:

( 6)( 5) ( 11) 17Q x x x x

a) - 27 b) 37 c) 13 d) - 13 e) 7

18 Sabiendo que: 2x2 - 3x = 18

calcular: ( 9)( 4) ( 3)( 5)A x x x x

a) - 6 b) 39 c) - 3 d) 6 e) - 34 19 Calcular:

( 1)( 4) ( 2)( 5) 2 ( 4) 9C x x x x x x

a) 10 b) - 12 c) 25 d) - 15 e) 12 20 Calcular:

2( 5)( 3) ( 7)( 9) 2 24A x x x x x x

a) 59 b) 80 c) 78 d) 94 e) 69

21 Calcular:

( 2)( 9) ( 4)( 7) 2 ( 2) 50T x x x x x x

a) 1 b) 2 c) 3 d) 4 e) 5

22 Siendo: 2

2 4 5x x Calcular:

( 7)( 1) ( 3)( 1) 8P x x x x

a) - 22 b) 21 c) 18 d) - 11 e) 10

23 Sabiendo que: 2

3 3 43x x

calcular:

( 2)( 5) ( 2)( 3) ( 1)( 6)P x x x x x x

a) 26 b) 48 c) 21 d) 22 e) 23

24 Sabiendo que: 2

2 19 14x x

Hallar:

( 2)( 7)( 1)( 5)Q x x x x

a) 6x b) 9x c) 4x d) 5x e) x

25 Si: 2

2 6 28x x Hallar:

( 9)( 2) ( 2)( 6)K x x x x

a) 13x b) 28x c) 17x d) 8x e) 6x

18



PRODUCTO DE UNA SUMA POR SU DIFERENCIA:

E J E R C I C I O S

( x + 3 ) ( x - 3 ) = ( x )2 - ( 3 )

2

= x2 - 9

( a - 2 ) ( a + 2 ) = ( a )2 - ( 2 )

2

= a2 - 4

( 7 m - 6 ) ( 7 m + 6 ) = ( 7m )2 - ( 6 )

2

= 49 m2 - 36

( 5 y2 - 2 m ) (5 y

2 + 2 m ) = ( 5 y

2 )

2 - ( 2 m )

2

= 25 y4 - 4 m

2

( a + b ) ( a - b ) = ( a )2 - ( b )

2

19



( 7)( 7)x x

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( 10)( 10)a a

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(2 9)(2 9)a a

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(1 )(1 )a a

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( 8)( 8)y y

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(5 )(5 )x x

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( 3 )( 3 )x y x y

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( 4)( 4)c c

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(8 1)(8 1)y y

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(4 )(4 )a c a c

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(5 3 )(5 3 )x x

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( 11)( 11)x x

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20



( 7 2)( 7 2)

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( 10 3)( 10 3)x x

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(4 3 2)(4 3 2)

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(3 2 1)(3 2 1)

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(2 9)(2 9)a a

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(1 2 )(1 2 )a a

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(3 8)(3 8)a a

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(5 2)(5 2)y y

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( 3 1)( 3 1)

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(7 5)(7 5)

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

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2 2(7 4)(7 4)x x

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21



01 Resolver:

2( 2)( 2)m m m

a) - 4 b) 8 c) 4 d) 2m2 e) 4m2

02 Reducir:

(5 )(5 ) ( 3)( 3) 1x x x x

a) - 14 b) 15 c) 25 d) - 8 e) 17 03 Reducir:

( 7)( 7) (2 )(2 ) 52x x x x

a) 9 b) - 11 c) 10 d) 7 e) 12 04 Calcular:

2( 1)( 1) ( 3)( 3) 2A x x x x x

a) 6 b) - 18 c) - 10 d) - 6 e) 10 05 Calcular:

( 7)( 7) ( 13 )( 13 ) 5R x x x x

a) 6 b) 10 c) 12 d) 9 e) 11 06 Calcular:

(5 1)(5 1) (5 3 )(5 3 ) 24M x x x x

a) 18x2 b) 16x2 c) 11x2 d) 9x2 e) 6x2

07 Hallar

H = ( x + 11 )( x - 11 ) + ( 15 - x )( 15 - x ) - 84

a) 14 b) 30 c) 24 d) 20 e) 25

08 Calcular:

2( 5)( 5) ( 9)( 9) 2 128F x x x x x

a) - 22 b) 70 c) 80 d) - 60 e) 22 09 Calcular:

2( 5)( 5) ( 1)( 1) 2 7S x x x x x

a) - 41 b) 12 c) 17 d) - 33 e) 28 10 Calcular:

( 2 7)( 2 7) (8 5)(8 5) 4T

a) - 50 b) 12 c) 49 d) - 25 e) 16 11 Calcular:

(4 6)(4 6) (2 3 1)(2 3 1) 2P

a) - 18 b) 19 c) 18 d) - 19 e) 37 12 Hallar

2( 4)( 4)

2(5 )(5 )

x x x

x x x

a)8

5 b)

4

5 c) -

16

25 d) - 5 e)

8

25

13 Reducir:

2( 5)( 5)( 25) 625G x x x

a) x4 b) 4x4 c) 4x2 d) 2x2 e) 2x4

14 Hallar:

8 2 2 4 ( 2)( 2)( 4) 16H x x x

a) x b) x4 c) 4x d) 4 e) 3

22



15 Calcular:

4 2 4 8 ( 1)( 1)( 1)( 1)( 1) 1C x x x x x

a) 1 b) x8 c) x4 d) 4x2 e) 2x4

16 Calcular:

2 4 (2 )(2 )(4 )M x x x x

a) 2 b) 8 c) 10 d) - 10 e) 4 17 Calcular:

2(2 5)(2 5)(4 25) 625Q x x x

a) 25 b) 5 - x4 c) 16x4 d) 16x8 e) 8x4

18 Calcular:

( 2)( 2) 4A x x

a) 8 b) x2 c) 16 d) x4 e) 4x4

19 Calcular:

4 2 3 2 3 4 6 8 12 24(2 )(2 )(2 )(2 )x x x x x

a) 10 b) 4 c) 16 d) 8 e) 12 20 Calcular:

8 4 3 4 3 8 6 12(3 2 )(3 2 )(3 2 ) 2

a) 9 b) 3 c) 18 d) 27 e) 1

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0000555122 Productos Notables