1. Ejercicio 211 del libro de Baldor
.( + ) =
( ) + 6( ) (2 ) + 15( ) (2 ) + 20( ) (2 ) + 15( ) (2 ) + 6( )(2 ) + (2 ) =
+6 (2 ) + 15 (4 ) + 20 (8 ) + 15 (16 ) + 6 (32 ) + 64 =
= + + + + + +
.( ! − # ) =
(2$ ) + 5(2$ ) (−3% ) + 10(2$ ) (−3% ) + 10(2$ ) (−3% ) + 5(2$ )(−3% ) +
(−3% ) =
32$&' + 5(16$( )(−3% ) + 10(8$ )(9% ) + 10(4$ )(−27%+ ) + 5(2$ )(81%& )−243%& =
32$&' + 80$( (−3% ) + 80$ (9% ) + 40$ (−27%+ ) + 10$ (81%& )−243%& =
= ! − !, # + - ! # − , ! # +, ! # − #
. (. + / ) =
(0 ) + 6(0 ) (1 ) + 15(0 ) (1 ) + 20(0 ) (1 ) + 15(0 ) (1 ) + 6(0 )(1 ) + (1 ) =
0 & + 6(0 &' )(1 ) + 15(0 ( )(1 ) + 20(0 )(1 + ) + 15(0 )(1& ) + 6(0 )(1& ) + (1 &( ) =
=. + . / + ., / + . / + . / + . / +/ ,
4.- ( - /- )- =
4.-
(3)3 + (3) (−1 3) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 )
+ (−1 3 )3 =
(3)3 + 7 (3) (−1 3 ) + 21(3) (−1 3 ) + 35(3) (−1 3 ) + 35(3) (−1 3 ) + 21(3) (−1 3 )
+ 7(3) (−1 3) + (−1 3)3 =
R= 2187 – 5103 /- + 5103
5103/ −2835
2835/
2835 945/
+ 945 ,
− 189
189/ 21/
+ 21 −/
5.-
5.- ( . − / ) =

2. (20 ) + (20 ) (−31 ) + (20 ) (−31 ) + (20 ) (−31 ) + (20 ) (−31 ) + (20 )
(−31 ) + (−3y ) =
(20 ) + 6(20 ) (−31 ) + 15(20 ) (−31 ) + 20(20 ) (−31 ) + 15(20 ) (−31 )
+ 6(20 ) (−31 ) + (−3y ) =
,
64.
R= 64 − - . / + 2160 /, −
2160. . / + 4860 . / − . / 729/
+ 729
6.-
6.- ( . + / ) =
& & & & &
( 7 ) + ( 0 ) (1 ) + ( 7 ) (8 ) + ( 7 ) (8 ) + ( 7 )(8 )
+ (1 ) =
& & & & &
( 7 ) + 5( 0 ) (1 ) + 10( 7 ) (8 ) + 10( 7 ) (8 ) + 5( 7 )(8 ) + (1 ) =
R= 9 + 9, : + 9 : + 9 : + 9 : +:
;
-. ( − <) =
= = = = = =
( ) + ( ) (− ) + ( ) (− ) + ( ) (− ) + ( ) (− ) + ( ) (− ) + (− ) =
> > > > > >
= = = = = =
( ) + 6 ( ) (− ) + 15( ) (− ) +20( ) (− ) + 15( ) (− ) + 6( ) (− ) +
> > > > >
(− ) =
>
; ; ; ; ; , ; -
= − + − + − +
- -< < < < < <
,. ( − . ), =
(1)( + (1)3 (−0 )+ (1) (−x4)2+ (1) (−x4)3+ (1) (−x4)4 + (1) (−x4)5+ (1) (−x4)6+
(1)(−x4)7+ (−x4)8 =
(1)( + 8(1)3 (−0 )+ 28(1) (−x4)2+ 56(1) (−x4)3+ 70(1) (−x4)4 +56(1) (−x4)5+
28(1) (−x4)6+ 8(1)( −x4)7+ (−x4)8 =
=1 – 8x4 + 28x8 – 56x12 + 70x16 – 56x20 + 28x24 – 8x28 + x32
1

3. .( − )7 =
. /
( )7 + ( )6 ( − )+( ) (− )2 + ( ) 4 (− )3 + ( )3 ( − )4 + ( ) 2 ( − )5 + ( )
@ @ A @ A @ A @ A @ A @
(− )6 + (− )7=
A A
(− ) 7 + 7( ) 6 (− ) + 21( ) (− )2 + 35( ) 4 (− )3 + 35( )3 ( − )4 + 21(− )2
A @ A @ A @ A @ A @
(− )5 + 7( )(− )6 + (− )7=
A @ A A
, - - - ,-
B= − + − + − + −
,-9 - 9 : 9 : 9 : 9 : ,9 : 9: ,: -
2 ! -
10. (
10. − ) =
m
2 2 $ 2 $ 2 $ 2 $
( )- + 7( ) (− ) + 21( ) (− ) + 35( ) (− ) + 35( ) (− )
$ $ 2 $ 2 $ 2 $ 2
2 $ 2 $ $
+21( ) (− ) + 7( )(− ) + (− )3 =
$ 2 $ 2 2
, , - !
R= - − + − - ! + ! − !, + ! −
! ! ! , ,
. (. + !#), =
(0 )( + 8(0 )3(3$%) + 28(0 ) ($%) + 56(0 ) ($%) + 70(0 ) ($%) +
56(0 ) ($%) + 28(0 ) ($%) + 8(0 )($%)3 + ($%)( =
0 + 80 & $% + 28(0&( )($ % ) + 56(0& )($ % ) + 70(0 & )($ % )
+56(0 + )($ % ) + 28(0 )($ % ) + 8(0 )($3 %3) + ($( %( ) =
=. + ,. !# + ,. , ! # + . ! # +- . ! # + . ! #
+ ,. ! # + ,. !- #- + !, #,
<
12.- (3− ) =
12.- (3
>D >D >D >D >D
(3)+ + 9(3)( (− ) + 36(3)3 (− ) + 84(3) (− ) + 126(3) (− ) + 126(3) (− ) +
>D >D >D >D
84(3) (− ) + 36(3) ( )3 + 9(3) (− )( + (− )+ =

4. >D >E >F >G >HI >HD >HE
19683 − 59049 + 78732 − 61236 + 30618 −10206 + 2268 − 324 + 27
+ 3 (& 3 + &(3
>HF >HG
− =
& &+ (
,< < < < ,
R= 19683 − 19683 < + 8748 < − 2268 < + 378 <, – 42 < + − -
+ − ,
13.- (1−
13.- (1 9 ) =
& & & & &
(1)&' + 10(1)+ (− ) + 45(1)( (− ) + 120(1)3 (− ) + 210(1) (− ) + 252(1) (− ) +
J J J J J
& & & & &
210 (1) (− ) + 120 (1) (− )3 + 45(1) (− )( + 10(1) (− )+ + (− )&' =
J J J J J
& & & & & & & & & &
1 − 10 + 45 D − 120 + 210 − 252 L + 210 F − 120 M + 45 G − 10 N + =
J J JK JE J J J J J JHI
R= 1 − 9
+9 − 9
+ 9
−
9
+ 9
−
9-
+ 9, − 9 + 9
.O ! − # P =
(2$ ) + 6(2$ ) (−5% ) + 15(2$ ) (−5% ) + 20(2$ ) (−5% ) + 15(2$ ) (−5% ) +
6(2$ )(−5% ) + (−5% ) =
64$& + 6(32$&' )(−5% ) + 15(16$( )(25%&' ) + 20(8$ )(−125%& ) + 15(4$ )(625% ' ) +
6(2$ )(−3125% ) + 15625% ' =
= ! − ! # + !, # − ! # + - ! # − - ! # +
#
.
.( − )- =
@ @ @ @ @
43 + 7( ) Q− R + 21(&) (− ) + 35( ) (− ) + 35( ) (− ) + 21( ) (− ) +
& & & &
@ @
7( )(− ) + (− )3 =
&
@ @ &' @& @ '
16384 + 7(4096) Q− R + 21(1024) Q& R + 35(256) Q− R + 35(64) Q R+
@ @ ' @
21(16) Q− R + 7(4) Q R−& =
&' '+ (
. . -. .
= , −- ,. + . − . + − + −
,