Comparte esto 👍👍DESCARGACAPITULO X Descomposición Factorial Ejercicio 96Factorar o descomponer en dos factores: a 4 + a 2 +1 = a 4 + a 2 + a 2 +1– a 2 =( a 4 +2 a 2 +1 ) – a 2 = ( a 2 +1 ) 2 – a 2 =[( a 2 +1 ) –a ] [( a 2 +1 ) +a ] =( a 2 –a+1 ) ( a 2 +a+1 ) m 4 + m 2 n 2 + n 4 = m 4 + m 2 n 2 + m 2 n 2 + n 4 – m 2 n 2 =( m 4 +2 m 2 n 2 + n 4 ) – m 2 n 2 = ( m 2 + n 2 ) 2 – m 2 n 2 =[( m 2 + n 2 ) –mn ] [( m 2 + n 2 ) +mn ] =( m 2 + n 2 –mn ) ( m 2 + n 2 +mn ) x 8 +3 x 4 +4 = x 8 +3 x 4 + x 4 +4– x 4 =( x 8 +4 x 4 +4 ) – x 4 = ( x 4 +2 ) 2 – x 4 =[( x 4 +2 ) – x 2 ] [( x 4 +2 ) + x 2 ] =( x 4 – x 2 +2 ) ( x 4 + x 2 +2 ) a 4 +2 a 2 +9 = a 4 +2 a 2 +4 a 2 +9–4 a 2 =( a 4 +6 a 2 +9 ) –4 a 2 = ( a 2 +3 ) 2 –4 a 2 =[( a 2 +3 ) –2a ] [( a 2 +3 ) +2a ] =( a 2 –2a+3 ) ( a 2 +2a+3 ) a 4 –3 a 2 b 2 + b 4 = a 4 –3 a 2 b 2 + a 2 b 2 + b 4 – a 2 b 2 =( a 4 –2 a 2 b 2 + b 4 ) – a 2 b 2 = ( a 2 – b 2 ) 2 – a 2 b 2 =[( a 2 – b 2 ) –ab ] [( a 2 – b 2 ) +ab ] =( a 2 –ab– b 2 ) ( a 2 +ab– b 2 ) x 4 –6 x 2 +1 = x 4 –6 x 2 +4 x 2 +1–4 x 2 =( x 4 –2 x 2 +1 ) –4 x 2 = ( x 2 –1 ) 2 –4 x 2 =[( x 2 –1 ) –2x ] [( x 2 –1 ) +2x ] =( x 2 –2x–1 ) ( x 2 +2x–1 ) 4 a 4 +3 a 2 b 2 +9 b 4 =4 a 4 +3 a 2 b 2 +9 a 2 b 2 +9 b 4 –9 a 2 b 2 =(4 a 4 +12 a 2 b 2 +9 b 4 ) –9 a 2 b 2 = (2 a 2 +3 b 2 ) 2 –9 a 2 b 2 =[(2 a 2 +3 b 2 ) –3ab ] [(2 a 2 +3 b 2 ) +3ab ] =(2 a 2 –3ab+3 b 2 ) (2 a 2 +3ab+3 b 2 ) 4 x 4 –29 x 2 +25 =4 x 4 –29 x 2 +9 x 2 +25–9 x 2 =(4 x 4 –20 x 2 +25 ) –9 x 2 = (2 x 2 –5 ) 2 –9 x 2 =[(2 x 2 –5 ) –3x ] [(2 x 2 –5 ) +3x ] =(2 x 2 –3x–5 ) (2 x 2 +3x–5 ) x 8 +4 x 4 y 4 +16 y 8 = x 8 +4 x 4 y 4 +4 x 4 y 4 +16 y 8 –4 x 4 y 4 =( x 8 +8 x 4 y 4 +16 y 8 ) –4 x 4 y 4 = ( x 4 +4 y 4 ) 2 –4 x 4 y 4 =[( x 4 +4 y 4 ) –2 x 2 y 2 ] [( x 4 +4 y 4 ) +2 x 2 y 2 ] =( x 4 –2 x 2 y 2 +4 y 4 ) ( x 4 +2 x 2 y 2 +4 y 4 ) 16 m 4 –25 m 2 n 2 +9 n 4 =16 m 4 –25 m 2 n 2 + m 2 n 2 +9 n 4 – m 2 n 2 =(16 m 4 –24 m 2 n 2 +9 n 4 ) – m 2 n 2 = (4 m 2 –3 n 2 ) 2 – m 2 n 2 =[(4 m 2 –3 n 2 ) –mn ] [(4 m 2 –3 n 2 ) +mn ] =(4 m 2 –mn–3 n 2 ) (4 m 2 +mn–3 n 2 ) 25 a 4 +54 a 2 b 2 +49 b 4 =25 a 4 +54 a 2 b 2 +16 a 2 b 2 +49 b 4 –16 a 2 b 2 =(25 a 4 +70 a 2 b 2 +49 b 4 ) –16 a 2 b 2 = (5 a 2 +7 b 2 ) 2 –16 a 2 b 2 =[(5 a 2 +7 b 2 ) –4ab ] [(5 a 2 +7 b 2 ) +4ab ] =(5 a 2 –4ab+7 b 2 ) (5 a 2 +4ab+7 b 2 ) 36 x 4 –109 x 2 y 2 +49 y 4 =36 x 4 –109 x 2 y 2 +25 x 2 y 2 +49 y 4 –25 x 2 y 2 =(36 x 4 –84 x 2 y 2 +49 y 4 ) –25 x 2 y 2 = (6 x 2 –7 y 2 ) 2 –25 x 2 y 2 =[(6 x 2 –7 y 2 ) –5xy ] [(6 x 2 –7 y 2 ) +5xy ] =(6 x 2 –5xy–7 y 2 ) (6 x 2 +5xy–7 y 2 ) 81 m 8 +2 m 4 +1 =81 m 8 +2 m 4 +16 m 4 +1–16 m 4 =(81 m 8 +18 m 4 +1 ) –16 m 4 = (9 m 4 +1 ) 2 –16 m 4 =[(9 m 4 +1 ) –4 m 2 ] [(9 m 4 +1 ) +4 m 2 ] =(9 m 4 –4 m 2 +1 ) (9 m 4 +4 m 2 +1 ) c 4 –45 c 2 +100 = c 4 –45 c 2 +25 c 2 +100–25 c 2 =( c 4 –20 c 2 +100 ) –25 c 2 = ( c 2 –10 ) 2 –25 c 2 =[( c 2 –10 ) –5c ] [( c 2 –10 ) +5c ] =( c 2 –5c–10 ) ( c 2 +5c–10 ) 4 a 8 –53 a 4 b 4 +49 b 8 =4 a 8 –53 a 4 b 4 +25 a 4 b 4 +49 b 8 –25 a 4 b 4 =(4 a 8 –28 a 4 b 4 +49 b 8 ) –25 a 4 b 4 = (2 a 4 –7 b 4 ) 2 –25 a 4 b 4 =[(2 a 4 –7 b 4 ) +5 a 2 b 2 ] [(2 a 4 –7 b 4 ) –5 a 2 b 2 ] =(2 a 4 +5 a 2 b 2 –7 b 4 ) (2 a 4 –5 a 2 b 2 –7 b 4 ) 49+76 n 2 +64 n 4 =49+76 n 2 +36 n 2 +64 n 4 –36 n 2 =(49+112 n 2 +64 n 4 ) –36 n 2 = (7+8 n 2 ) 2 –36 n 2 =[(7+8 n 2 ) –6n ] [(7+8 n 2 ) +6n ] =(7–6n+8 n 2 ) (7+6n+8 n 2 ) 25 x 4 –139 x 2 y 2 +81 y 4 =25 x 4 –139 x 2 y 2 +49 x 2 y 2 +81 y 4 –49 x 2 y 2 =(25 x 4 –90 x 2 y 2 +81 y 4 ) –49 x 2 y 2 = (5 x 2 –9 y 2 ) 2 –49 x 2 y 2 =[(5 x 2 –9 y 2 ) –7xy ] [(5 x 2 –9 y 2 ) +7xy ] =(5 x 2 –7xy–9 y 2 ) (5 x 2 +7xy–9 y 2 ) 49 x 8 +76 x 4 y 4 +100 y 8 =49 x 8 +76 x 4 y 4 +64 x 4 y 4 +100 y 8 –64 x 4 y 4 =(49 x 8 +140 x 4 y 4 +100 y 8 ) –64 x 4 y 4 = (7 x 4 +10 y 4 ) 2 –64 x 4 y 4 =[(7 x 4 +10 y 4 ) –8 x 2 y 2 ] [(7 x 4 +10 y 4 ) +8 x 2 y 2 ] =(7 x 4 –8 x 2 y 2 +10 y 4 ) (7 x 4 +8 x 2 y 2 +10 y 4 ) 4–108 x 2 +121 x 4 =4–108 x 2 +64 x 2 +121 x 4 –64 x 2 =(4–44 x 2 +121 x 4 ) –64 x 2 = (2–11 x 2 ) 2 –64 x 2 =[(2–11 x 2 ) –8x ] [(2–11 x 2 ) +8x ] =(2–8x–11 x 2 ) (2+8x–11 x 2 ) 121 x 4 –133 x 2 y 4 +36 y 8 =121 x 4 –133 x 2 y 4 + x 2 y 4 +36 y 8 – x 2 y 4 =(121 x 4 –132 x 2 y 4 +36 y 8 ) – x 2 y 4 = (11 x 2 –6 y 4 ) 2 – x 2 y 4 =[(11 x 2 –6 y 4 ) –x y 2 ] [(11 x 2 –6 y 4 ) +x y 2 ] =(11 x 2 –x y 2 –6 y 4 ) (11 x 2 +x y 2 –6 y 4 ) 144+23 n 6 +9 n 12 =144+23 n 6 +49 n 6 +9 n 12 –49 n 6 =144+72 n 6 +9 n 12 –49 n 6 = (12+3 n 6 ) 2 –49 n 6 =[(12+3 n 6 ) –7 n 3 ] [(12+3 n 6 ) +7 n 3 ] =(12–7 n 3 +3 n 6 ) (12+7 n 3 +3 n 6 ) 16–9 c 4 + c 8 =16–9 c 4 + c 4 + c 8 – c 4 =(16–8 c 4 + c 8 ) – c 4 = (4– c 4 ) 2 – c 4 =[(4– c 4 ) – c 2 ] [(4– c 4 ) + c 2 ] =(4– c 2 – c 4 ) (4+ c 2 – c 4 ) 64 a 4 –169 a 2 b 4 +81 b 8 =64 a 4 –169 a 2 b 4 +25 a 2 b 4 +81 b 8 –25 a 2 b 4 =(64 a 4 –144 a 2 b 4 +81 b 8 ) –25 a 2 b 4 = (8 a 2 –9 b 4 ) 2 –25 a 2 b 4 =[(8 a 2 –9 b 4 ) –5a b 2 ] [(8 a 2 –9 b 4 ) +5a b 2 ] =(8 a 2 –5a b 2 –9 b 4 ) (8 a 2 +5a b 2 –9 b 4 ) 225+5 m 2 + m 4 =225+5 m 2 +25 m 2 + m 4 –25 m 2 =(225+30 m 2 + m 4 ) –25 m 2 = (15+ m 2 ) 2 –25 m 2 =[(15+ m 2 ) –5m ] [(15+ m 2 ) +5m ] =(15–5m+ m 2 ) (15+5m+ m 2 ) 1–126 a 2 b 4 +169 a 4 b 8 =1–126 a 2 b 4 +100 a 2 b 4 +169 a 4 b 8 –100 a 2 b 4 =(1–26 a 2 b 4 +169 a 4 b 8 ) –100 a 2 b 4 = (1–13 a 2 b 4 ) 2 –100 a 2 b 4 =[(1–13 a 2 b 4 ) –10a b 2 ] [(1–13 a 2 b 4 ) +10a b 2 ] =(1–10a b 2 –13 a 2 b 4 ) (1+10a b 2 –13 a 2 b 4 ) x 4 y 4 +21 x 2 y 2 +121 = x 4 y 4 +21 x 2 y 2 + x 2 y 2 +121– x 2 y 2 =( x 4 y 4 +22 x 2 y 2 +121 ) – x 2 y 2 = ( x 2 y 2 +11 ) 2 – x 2 y 2 =[( x 2 y 2 +11 ) +xy ] [( x 2 y 2 +11 ) –xy ] =( x 2 y 2 +xy+11 ) ( x 2 y 2 –xy+11 ) 49 c 8 +75 c 4 m 2 n 2 +196 m 4 n 4 =49 c 8 +75 c 4 m 2 n 2 +121 c 4 m 2 n 2 +196 m 4 n 4 –121 c 4 m 2 n 2 =49 c 8 +196 c 4 m 2 n 2 +196 m 4 n 4 –121 c 4 m 2 n 2 = (7 c 4 +14 m 2 n 2 ) 2 –121 c 4 m 2 n 2 =[(7 c 4 +14 m 2 n 2 ) –11 c 2 mn ] [(7 c 4 +14 m 2 n 2 ) +11 c 2 mn ] =(7 c 4 –11 c 2 mn+14 m 2 n 2 ) (7 c 4 +11 c 2 mn+14 m 2 n 2 ) 81 a 4 b 8 –292 a 2 b 4 x 8 +256 x 16 =81 a 4 b 8 –292 a 2 b 4 x 8 +4 a 2 b 4 x 8 +256 x 16 –4 a 2 b 4 x 8 =(81 a 4 b 8 –288 a 2 b 4 x 8 +256 x 16 ) –4 a 2 b 4 x 8 = (9 a 2 b 4 –16 x 8 ) 2 –4 a 2 b 4 x 8 =[(9 a 2 b 4 –16 x 8 ) –2a b 2 x 4 ] [(9 a 2 b 4 –16 x 8 ) +2a b 2 x 4 ] =(9 a 2 b 4 –2a b 2 x 4 –16 x 8 ) (9 a 2 b 4 +2a b 2 x 4 –16 x 8 ) Categories: Capítulo X