1. The document contains examples of polynomial expressions being expanded. 2. It provides the step-by-step work of expanding polynomials with degree up to 8. 3. The expansions involve multiple terms with coefficients and variables being combined.

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$% =
+
= − " +, " − + " ++ " − "
. (- + . ) =
(/ ) + 6(/ ) (0 ) + 15(/ ) (0 ) + 20(/ ) (0 ) + 15(/ ) (0 ) + 6(/ )(0 ) + (0 ) =
/ % + 6(/ %& )(0 ) + 15(/ ' )(0 ) + 20(/ )(0 * ) + 15(/ )(0% ) + 6(/ )(0% ) + (0 %' ) =
=- + - . + -+ . + - . + - . + - . +. +
4.- ( - ., ), =
4.-
(3)3 + (3) (-0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 )
+ (−0 3 )3 =
(3)3 + 7 (3) (−0 3 ) + 21(3) (−0 3 ) + 35(3) (−0 3 ) + 35(3) (−0 3 ) + 21(3) (−0 3 )
+ 7(3) (−0 3) + (−0 3)3 =
R= 2187 – 5103 ., + 5103
5103. −2835
2835.
2835 945.
+ 945 +
− 189
189. 21.
+ 21 −.

2. 5.-
5.- ( - − . ) =
(2/ ) + (2/ ) (−30 ) + (2/ ) (−30 ) + (2/ ) (−30 ) + (2/ ) (−30 ) + (2/ )
(−30 ) + (−3y ) =
(2/ ) + 6(2/ ) (−30 ) + 15(2/ ) (−30 ) + 20(2/ ) (−30 ) + 15(2/ ) (−30 )
+ 6(2/ ) (−30 ) + (−3y ) =
+
64-
R= 64 − , - . + 2160 .+ −
2160- - . + 4860 - . − - . 729.
+ 729
6.-
6.- ( - + . ) =
% % % % %
( 7 ) + ( / ) (0 ) + ( 7 ) (8 ) + ( 7 ) (8 ) + ( 7 )(8 )
+ (0 ) =
% % % % %
( 7 ) + 5( / ) (0 ) + 10( 7 ) (8 ) + 10( 7 ) (8 ) + 5( 7 )(8 ) + (0 ) =
R= 9 + 9+ : + 9 : + 9 : + 9 : +:
;
,. ( − <) =
= = = = = =
( ) - ( ) ( )+( ) ( ) -( ) ( ) +( ) ( ) - ( )( ) +( ) =
> > > > > >
= = = = = =
( ) - 6 ( ) ( ) + 15( ) ( ) - 20( ) ( ) + 15( ) ( ) - 6( ) ( ) + ( ) =
> > > > > >
; ; ; ; ; + ; ,
=, − ,<
+ < − <
+ <
− <
+ <
+. ( − - )+ =
(1)' - (1)3 (x) + (1) (x4)2- (1) (x4)3+ (1) (x4)4- (1) (x4)5+ (1) (x4)6- (1)(x4)7+ (x4)8 =
(1)' - 8(1)3 (x) + 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
.( - )7 =
- .

3. ( )7 – ( )6 ( )+( ) ( )2 – ( )4 ( )3 + ( )3 ( )4 – ( ) 2 ( )5 + ( ) ( )6 –
@ @ A @ A @ A @ A @ A @ A
( )7=
A
( ) 7 – 7( ) 6 ( ) + 21( ) ( )2 – 35( )4 ( )3 + 35( )3 ( )4 – 21( ) 2 ( )5 +
@ @ A @ A @ A @ A @ A
7( )( )6 – ( )7=
@ 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= , − + −, + − + −
+ +
. (- + ")+
(/ )' + 8(/ )3(3#$) + 28(/ ) (#$) + 56(/ ) (#$) + 70(/ ) (#$) +
56(/ ) (#$) + 28(/ ) (#$) + 8(/ )(#$)3 + (#$)' =
/ + 8/ % #$ + 28(/%' )(# $ ) + 56(/% )(# $ ) + 70(/ % )(# $ )
+56(/ * )(# $ ) + 28(/ )(# $ ) + 8(/ )(#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) (− )' − (− )* =
>D >E >F >G >HI >HD >HE
19683 − 59049 + 78732 *
− 61236 3
+ 30618 '% −10206 + 2268 3 *
− 324 %'3
+ 27
>HF >HG
%
− %* ' =

4. + +
+
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) (− J) − 120 (1) (− J)3 + 45(1) (− J)' − 10(1) (− 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−%
%& &* '
- - ,- -
= + −, +- + - − - + − + − +