Ejercicio 211 del libro de baldor
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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.
Ejercicio 211 del libro de baldor
- 1. Ejercicio 211 del libro de Baldor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¨C 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 ¨C 8x4 + 28x8 ¨C 56x12 + 70x16 ¨C 56x20 + 28x24 ¨C 8x28 + x32 1 .( - )7 = - .
- 3. ( )7 ¨C ( )6 ( )+( ) ( )2 ¨C ( )4 ( )3 + ( )3 ( )4 ¨C ( ) 2 ( )5 + ( ) ( )6 ¨C @ @ A @ A @ A @ A @ A @ A ( )7= A ( ) 7 ¨C 7( ) 6 ( ) + 21( ) ( )2 ¨C 35( )4 ( )3 + 35( )3 ( )4 ¨C 21( ) 2 ( )5 + @ @ A @ A @ A @ A @ A 7( )( )6 ¨C ( )7= @ A A + , , , +, B= - + ? + ? + ? +,9 , 9 : 9 : 9 : 9 : +9 : 9: +: , 2 10. 10. ( - ), m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
- 4. + + + R= 19683 ? 19683 + 8748 ? 2268 + 378 ¨C 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?% %& &* ' - - ,- - = + ?, +- + - ? - + ? + ? +