1. The document contains 6 multi-step polynomial expressions involving variables x and y. Each expression is set equal to an algebraic solution involving terms of the variables. 2. Steps are shown to solve for each expression, expanding polynomials and grouping like terms. Solutions simplify the expressions and are presented with the variables. 3. The document demonstrates solving higher order polynomial expressions through expanding, ordering terms, and simplifying to isolated solutions involving the variables.

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−& =
&' '+ (
. . -. .
= , −- ,. + . − . + − + −
,