Ejercicio 13 del libro de álgebra de Baldor

Tarea 2 Valor numérico de expresiones expresiones compuestas

Ejercicio 13

Hallar el valor numérico de las expresiones siguientes, para: 1 2 1 a = 1, b = 2, c = 3, d  = 4, m = , n = ,  p = , x = 0 2 3 4 1

( a + b) c − d  =

2

( a + b)(b − a) =

3

(b − m)(c − n) + 4a 2

4

( 2m + 3n)( 4 p + b 2 ) =

5

( 4m + 8 p )(a 2

6

(c − b)(d  − c)(b − a )(m − p ) =

7

b 2 (c + d ) − a 2 ( m + n) + 2 x =

8

2mx + 6(b 2

9

 8m + 16 p  a =     9n b  

10

 x + m( a b

11

4(m +  p) a

=

+ b 2 )(6n − d ) =

+ c2 ) − 4d 2 =

+ d c − c a ) =

÷

a

+ b2 = 2

2

c

12

( 2m + 3n + 4 p )(8 p + 6n − 4m)(9n + 20 p) =

13

c 2 ( m + n) − d 2 (m +  p) + b 2 (n +  p) =

14

     

15

c2

17

   m = d     

2

a

( 4 p + 2b)(18n − 24 p) + 2(8m + 2)( 40 p + a ) = a+

16

+ d 2 ÷

d 

b d  − b

×

5+

( a + b) c 2

2 m2

 p 2

=

+ 8b − m

n2

=

18

19

    

a+c

2

6n  

6abc 2 8b

+

   ÷ (c + d )  

b

3( c − b) 32m

20

21

+

− 2(d  − a)

3mn 2( b − a )

 p

16 p

= −2= n

− cdnp = abc

+ b2 + a + b a + b = 3( )(2 3 ) 2 2 b −a a

2

2

2

1 1   1 1    1 1   +    +   +  +  +   =  a b   b c    n m  

22

b

23

( 2m + 3n)(4 p + 2c ) − 4m 2 n 2 b

24

2

−

=

c

3 2ab − m

−

n b−m

=

RESPUESTAS

1

( a + b) c − d  =

(1 + 2 3 − 4 = 3 ⋅ 3 − 4 = 9 − 4 = 5 2

( a + b)(b − a) = (1 + 2)(2 − 1) = 3 ⋅ 1 = 3

3

(b − m)(c − n) + 4a 2

=  2 − 1   3 − 2  + 4 ⋅ 12 =  4 − 1   9 − 2  + 4 =  3   7  + 4 = 21 + 4 = 7 + 4 = 7 + 8 = 15 = 7 1                2 6 2 2 2   2    3     2    3    2   3  

4

( 2m + 3n)( 4 p + b 2 ) =

 2 ⋅ 1 + 3 ⋅ 2   4 ⋅ 1 + 22  =  2 + 6   4 + 4  = (1 + 2 ()1 + 4 ) = 3 ⋅ 5 = 15           3    4   2    2 3   4  

5

6

( 4m + 8 p )(a 2

+ b 2 )(6n − d ) =  4 ⋅ 1 + 8 ⋅ 1  (12 + 22  6) ⋅ 2 − 4  =  4 + 8  (1 + 4  ) 12 − 4  = ( 2 + 2 5)( 4)(− 4 = 4) ⋅ 5 ⋅ 0 = 0             4     2   3    2 4     3   (c − b)(d  − c)(b − a )(m − p ) = 1 1    2 − 1  = 1 ( 3 − 2 4)( − 3 2 −)( 1    −)  = 1⋅1⋅1⋅   

 2

7

2

10

1 2

 2

3  

4

 

6

 

6

6

6

6

+ c2 ) − 4d 2 =

⋅ 0 + 6( 22 + 32 − 4 ⋅ 42 = 6( 4 + 9 )− 4 ⋅16 = 6 ⋅ 13 − 64 = 78 − 64 = 14

 x + m( a b

1 2

(12

+ d c − c a ) = + 43 − 31 ) = 1 (1 + 64 − 3 =) 1 ⋅ 62 = 62 = 31

4(m +  p)

2

÷

a

2

2

2

+ b2 = 2

a c  1 1   4 +   2 2  2 4  ÷ 1 + 2 1 32

12

 

 8m + 16 p  a =     9n b    8 ⋅ 1 16 ⋅ 1     8 16          4 4   2 2 4 2 4   ⋅ 1 =  +  =  +  = + 2 = 2 + 6 = 8 = 2 2 + 18 2   2    6 2   3 3 3 3  9 ⋅ 2        3     3  

0+

11

4

1 2    3 + 4  = 28 − 7 = 168 − 7 = 161 = 26 5 )− 12    +  + 2 ⋅ 0 = 4 ⋅ 7 − 1  

2mx + 6(b 2 2⋅

9

 

b 2 (c + d ) − a 2 ( m + n) + 2 x =

2 (3 + 4

8

4  

2 + 1   1 + 4 = 4  = 4 ⋅ 3 ÷ 5 = 12 ÷ 5 = 12 ⋅ 9 = 108 = 27 = 5 2   ÷ 4 9 4 9 4 5 20 5 5   4   9

( 2m + 3n + 4 p )(8 p + 6n − 4m)(9n + 20 p) =

 2 ⋅ 1 + 3 ⋅ 2 + 4 ⋅ 1   8 ⋅ 1 + 6 ⋅ 2 − 4 ⋅ 1   9 ⋅ 2 + 20 ⋅ 1  =  2 + 6 + 4   8 + 12 − 4   18 + 20  =               3 4    4 3 2    3 4    2 3 4   4 3 2    3 4     2 (1 + 2 + 1 2)+( 4 − 2 6 + 5)( = 4 ⋅ 4 )⋅ 11 = 176 13

c 2 ( m + n) − d 2 (m +  p) + b 2 ( n +  p) =

 1 + 2  − 42  1 + 1  + 22  2 + 1  = 9 3 + 4  − 16 2 + 1  + 4 8 + 3  = 9 ⋅ 7 − 16 ⋅ 3 + 4 11 =                  6 4 12  2 3    2 4    3 4     6     4     12   − + 63 48 44 21 − + = − 12 + 44 = 126 144 44 = 26 = 2 2 = 2 1

32 

6

14

15

           

c2

4

12

+ d 2

   m = d      2   1   ÷   ⋅ =    4   2   ÷

a

+ 42

32

1

2

12

12

12

12

6

2

9 + 16 1

  1   ÷ 2   ⋅ =    2   2  

25 1

  1 1 5 1 ÷ 1  ⋅ = ⋅ = = 5 2   2 2 2 2  

( 4 p + 2b)(18n − 24 p) + 2(8m + 2)( 40 p + a ) =

 4 ⋅ 1 + 2 ⋅ 2   18 ⋅ 2 − 24 ⋅ 1  + 2 8 ⋅ 1 + 2   40 1 + 1 =           3 4 2 4   4              4 + 4   36 − 24  + 2 8 + 2   40 + 1 = (1 + 4 12 )( − 6 + 2) 4 + 2(           4 3 4 2 4               ( 5 )( 6 ) + 2 6( )11 ( =) 30 + 2 ⋅ 66 = 30 + 132 = 162

a+ 16

d 

b d  − b

×

5+

m2

=

2 2

 1       2   = 1 + 2 × 2× 2 4−2 2  1       4  

1+

17

4

( a + b) c 2 (1 + 2) 3

2

)

2

 p 2

5+

10 + 1)( =

+ 8b − m + 8⋅ 2 −

1 2

n2

5+

2 1 4

1 6

= 3×5 2

+8 1

= 3 × 13 = 3 ⋅ 208 = 624 = 312 2

6

1

2

2

6

= 2

 2   = 3 ⋅     3  

9 + 16 −

1 2

⋅ = 3⋅

2 3

25 −

3 6

= 3 ⋅ 5 − 1 = 45 3

−1

3

= 44 = 14 2 3

3

18

19

  a + c    + 6n    ÷ (c + d )  p = b 2          2     6      1+ 3 3    1  4    2 + 2  ÷ (3 + 4) 4 =  2 +              3( c − b) 32m 3( 3 − 2

− 2(d  − a)

16 p

12 3 2

    2 2   7 7 7 4  ÷ 7 ⋅ 1 =   ( + ÷ = 1 + 1 )÷ = 2 ÷ =      2  2 2   2 2 2 7    

−2= n

1

1

2

4

) 32 ⋅ − 2(4 − 1) 16 ⋅ −

2 2

= 3 ⋅1⋅

32 2

− 2⋅3⋅

16 4

− 6 = 3⋅ 2

16 − 6 ⋅ 4

−3=

3 3 ⋅ 4 − 6 ⋅ 2 − 3 = 12 − 12 − 3 = 12 − 15 = −3

6abc

20

2 8b

+

3mn 2( b − a )

6 ⋅1⋅ 2 ⋅ 3 2 8⋅2 6

2

3

abc

1 2

⋅

2 3 2( 2 − 1)

+ 1 − 1 = 18

8

21

+

3⋅

− cdnp =

+ 12 − 8 24

−

3⋅ 4⋅

⋅

3 4 1⋅ 2 ⋅ 3

= 30

−8

24

23

=

36 2 16

+

6 2(1)

24

− 12 = 6

6 2⋅4

+

1 2

−2= 6

= 22 = 11 24

12

+ b 2 + 3(a + b)(2a + 3b) = 2 2 b −a 2 2 1 +2 1+ 4 5 5 5 + 216 221 2 3 ( 1 2 )( 2 1 3 2 ) 3 3 ( 2 6 ) 3 3 8 72 73 + + ⋅ + ⋅ = + ⋅ + = + ⋅ ⋅ = + = = = 22 − 12 4 −1 3 3 3 3 3 a

2

2

22

6

2 1

 1 1   1 1    1 1   b +  +   +  +  +   =  a b   b c    n m   2     2 1 1   1 1    1 1   2 + 1   3 + 2    3 2       2 2 +  +   +  +  +   = 4 +     +  +   = 2    6    2 1    1 2   2 3    2 1        3 2   2 2 3   5    3 + 4   15    7   5 49 16 + 5 + 49 70 35     = = =71 4 +     +    = 4 +   +    = 4 + + = 4 2 4 4 2 2  2   6     2    12    2   2

( 2m + 3n)(4 p + 2c ) − 4m 2n 2

=

2

2

 2 ⋅ 1 + 3 ⋅ 2   4 ⋅ 1 + 2 ⋅ 3 − 4 ⋅  1    2   =            3    4   2    2    3    2 + 6   4 + 6  − 4 ⋅ 1 ⋅ 4 = (1 + 2 ()1 + 6 )− 16 = 3 ⋅ 7 − 4 = 21 − 4 = 189 − 4 = 185 = 20 5      36 9 9 9 9 9  2 3   4   4 9

b

24

2

−

c

3 2ab − m 3 22 − 3

−

2 ⋅1⋅ 2 −

1 2

n b−m 2

−

=

3 2−

1 2

=

4 −1 1 4− 2

2

−

3

4 −1 2

2

=

3 8 −1 2

−3= 3

3 7

2

2

− 4 = 6 − 4 = 54 9

7

9

− 28

63

= 26 63