Comparte esto 👍👍DESCARGACAPITULO X Descomposición Factorial Ejercicio 95Factorar o descomponer en dos factores: a 2 +2ab+ b 2 – x 2 = (a+b ) 2 – x 2 =[(a+b ) +x ] [(a+b ) –x ] =(a+b+x ) (a+b–x ) x 2 –2xy+ y 2 – m 2 = (x–y ) 2 – m 2 =[(x–y ) +m ] [(x–y ) –m ] =(x–y+m ) (x–y–m ) m 2 +2mn+ n 2 –1 = (m+n ) 2 –1 =[(m+n ) –1 ] [(m+n ) +1 ] =(m+n–1 ) (m+n+1 ) a 2 –2a+1– b 2 = (a–1 ) 2 – b 2 =[(a–1 ) +b ] [(a–1 ) –b ] =(a+b–1 ) (a–b–1 ) n 2 +6n+9– c 2 = (n+3 ) 2 – c 2 =[(n+3 ) –c ] [(n+3 ) +c ] =(n–c+3 ) (n+c+3 ) a 2 + x 2 +2ax–4 = a 2 +2ax+ x 2 –4 = (a+x ) 2 –4 =[(a+x ) –2 ] [(a+x ) +2 ] =(a+x–2 ) (a+x+2 ) a 2 +4–4a–9 b 2 = a 2 –4a+4–9 b 2 = (a–2 ) 2 –9 b 2 =[(a–2 ) +3b ] [(a–2 ) –3b ] =(a+3b–2 ) (a–3b–2 ) x 2 +4 y 2 –4xy–1 = x 2 –4xy+4 y 2 –1 = (x–2y ) 2 –1 =[(x–2y ) –1 ] [(x–2y ) +1 ] =(x–2y–1 ) (x–2y+1 ) a 2 –6ay+9 y 2 –4 x 2 = (a–3y ) 2 –4 x 2 =[(a–3y ) –2x ] [(a–3y ) +2x ] =(a–2x–3y ) (a+2x–3y ) 4 x 2 +25 y 2 –36+20xy =4 x 2 +20xy+25 y 2 –36 = (2x+5y ) 2 –36 =[(2x+5y ) –6 ] [(2x+5y ) +6 ] =(2x+5y–6 ) (2x+5y+6 ) 9 x 2 –1+16 a 2 –24ax =9 x 2 –24ax+16 a 2 –1 = (3x–4a ) 2 –1 =[(3x–4a ) –1 ] [(3x–4a ) +1 ] =(3x–4a–1 ) (3x–4a+1 ) 1+64 a 2 b 2 – x 4 –16ab =1–16ab+64 a 2 b 2 – x 4 = (1–8ab ) 2 – x 4 =[(1–8ab ) + x 2 ] [(1–8ab ) – x 2 ] =(1–8ab+ x 2 ) (1–8ab– x 2 ) a 2 – b 2 –2bc– c 2 = a 2 –( b 2 +2bc+ c 2 ) = a 2 – (b+c ) 2 =[a+(b+c ) ] [a–(b+c ) ] =(a+b+c ) (a–b–c ) 1– a 2 +2ax– x 2 =1–( a 2 –2ax+ x 2 ) =1– (a–x ) 2 =[1–(a–x ) ] [1+(a–x ) ] =(1–a+x ) (1+a–x ) m 2 – x 2 –2xy– y 2 = m 2 –( x 2 +2xy+ y 2 ) = m 2 – (x+y ) 2 =[m–(x+y ) ] [m+(x+y ) ] =(m–x–y ) (m+x+y ) c 2 – a 2 +2a–1 = c 2 –( a 2 –2a+1 ) = c 2 – (a–1 ) 2 =[c–(a–1 ) ] [c+(a–1 ) ] =(c–a+1 ) (c+a–1 ) 9– n 2 –25–10n =9– n 2 –10n–25 =9–( n 2 +10n+25 ) =9– (n+5 ) 2 =[3–(n+5 ) ] [3+(n+5 ) ] =(3–n–5 ) (3+n+5 ) =(–2–n ) (n+8 ) =–(n+2 ) (n+8 ) 4 a 2 – x 2 +4x–4 =4 a 2 –( x 2 –4x+4 ) =4 a 2 – (x–2 ) 2 =[2a–(x–2 ) ] [2a+(x–2 ) ] =(2a–x+2 ) (2a+x–2 ) 1– a 2 –9 n 2 –6an =1– a 2 –6an–9 n 2 =1–( a 2 +6an+9 n 2 ) =1– (a+3n ) 2 =[1–(a+3n ) ] [1+(a+3n ) ] =(1–a–3n ) (1+a+3n ) 25– x 2 –16 y 2 +8xy =25– x 2 +8xy–16 y 2 =25–( x 2 –8xy+16 y 2 ) =25– (x–4y ) 2 =[5+(x–4y ) ] [5–(x–4y ) ] =(5+x–4y ) (5–x+4y ) 9 x 2 – a 2 –4 m 2 +4am =9 x 2 – a 2 +4am–4 m 2 =9 x 2 –( a 2 –4am+4 m 2 ) =9 x 2 – (a–2m ) 2 =[3x–(a–2m ) ] [3x+(a–2m ) ] =(3x–a+2m ) (3x+a–2m ) 16 x 2 y 2 +12ab–4 a 2 –9 b 2 =16 x 2 y 2 –4 a 2 +12ab–9 b 2 =16 x 2 y 2 –(4 a 2 –12ab+9 b 2 ) =16 x 2 y 2 – (2a–3b ) 2 =[4xy–(2a–3b ) ] [4xy+(2a–3b ) ] =(4xy–2a+3b ) (4xy+2a–3b ) – a 2 +25 m 2 –1–2a =25 m 2 – a 2 –2a–1 =25 m 2 –( a 2 +2a+1 ) =25 m 2 – (a+1 ) 2 =[5m–(a+1 ) ] [5m+(a+1 ) ] =(5m–a–1 ) (5m+a+1 ) 49 x 4 –25 x 2 –9 y 2 +30xy =49 x 4 –25 x 2 +30xy–9 y 2 =49 x 4 –(25 x 2 –30xy+9 y 2 ) =49 x 4 – (5x–3y ) 2 =[7 x 2 –(5x–3y ) ] [7 x 2 +(5x–3y ) ] =(7 x 2 –5x+3y ) (7 x 2 +5x–3y ) a 2 –2ab+ b 2 – c 2 –2cd– d 2 =( a 2 –2ab+ b 2 ) –( c 2 +2cd+ d 2 ) = (a–b ) 2 – (c+d ) 2 =[(a–b ) +(c+d ) ] [(a–b ) –(c+d ) ] =(a–b+c+d ) (a–b–c–d ) x 2 +2xy+ y 2 – m 2 +2mn– n 2 =( x 2 +2xy+ y 2 ) –( m 2 –2mn+ n 2 ) = (x+y ) 2 – (m–n ) 2 =[(x+y ) –(m–n ) ] [(x+y ) +(m–n ) ] =(x+y–m+n ) (x+y+m–n ) a 2 +4 b 2 +4ab– x 2 –2ax– a 2 =( a 2 +4ab+4 b 2 ) –( x 2 +2ax+ a 2 ) = (a+2b ) 2 – (x+a ) 2 =[(a+2b ) –(x+a ) ] [(a+2b ) +(x+a ) ] =( a +2b–x– a ) (a+2b+x+a ) =(2b–x ) (2a+2b+x ) x 2 +4 a 2 –4ax– y 2 –9 b 2 +6by =( x 2 –4ax+4 a 2 ) –( y 2 –6by+9 b 2 ) = (x–2a ) 2 – (y–3b ) 2 =[(x–2a ) –(y–3b ) ] [(x–2a ) +(y–3b ) ] =(x–2a–y+3b ) (x–2a+y–3b ) m 2 – x 2 +9 n 2 +6mn–4ax–4 a 2 =( m 2 +6mn+9 n 2 ) –( x 2 +4ax+4 a 2 ) = (m+3n ) 2 – (x+2a ) 2 =[(m+3n ) –(x+2a ) ] [(m+3n ) +(x+2a ) ] =(m+3n–x–2a ) (m+3n+x+2a ) 9 x 2 +4 y 2 – a 2 –12xy–25 b 2 –10ab =(9 x 2 –12xy+4 y 2 ) –( a 2 +10ab+25 b 2 ) = (3x–2y ) 2 – (a+5b ) 2 =[(3x–2y ) –(a+5b ) ] [(3x–2y ) +(a+5b ) ] =(3x–2y–a–5b ) (3x–2y+a+5b ) 2am– x 2 –9+ a 2 + m 2 –6x =( a 2 +2am+ m 2 ) –( x 2 +6x+9 ) = (a+m ) 2 – (x+3 ) 2 =[(a+m ) –(x+3 ) ] [(a+m ) +(x+3 ) ] =(a+m–x–3 ) (a+m+x+3 ) x 2 –9 a 4 +6 a 2 b+1+2x– b 2 =( x 2 +2x+1 ) –(9 a 4 –6 a 2 b+ b 2 ) = (x+1 ) 2 – (3 a 2 –b ) 2 =[(x+1 ) –(3 a 2 –b ) ] [(x+1 ) +(3 a 2 –b ) ] =(x+1–3 a 2 +b ) (x+1+3 a 2 –b ) 16 a 2 –1–10m+9 x 2 –24ax–25 m 2 =(16 a 2 –24ax+9 x 2 ) –(25 m 2 +10m+1 ) = (4a–3x ) 2 – (5m+1 ) 2 =[(4a–3x ) +(5m+1 ) ] [(4a–3x ) –(5m+1 ) ] =(4a–3x+5m+1 ) (4a–3x–5m–1 ) 9 m 2 – a 2 +2acd– c 2 d 2 +100–60m =(9 m 2 –60m+100 ) –( a 2 –2acd+ c 2 d 2 ) = (3m+10 ) 2 – (a–cd ) 2 =[(3m+10 ) –(a–cd ) ] [(3m+10 ) +(a–cd ) ] =(3m+10–a+cd ) (3m+10+a–cd ) 4 a 2 –9 x 2 +49 b 2 –30xy–25 y 2 –28ab =(4 a 2 –28ab+49 b 2 ) –(9 x 2 +30xy+25 y 2 ) = (2a–7b ) 2 – (3x+5y ) 2 =[(2a–7b ) –(3x+5y ) ] [(2a–7b ) +(3x+5y ) ] =(2a–7b–3x–5y ) (2a–7b+3x+5y ) 225 a 2 –169 b 2 +1+30a+26bc– c 2 =(225 a 2 +30a+1 ) –(169 b 2 –26bc+ c 2 ) = (15a+1 ) 2 – (13b–c ) 2 =[(15a+1 ) –(13b–c ) ] [(15a+1 ) +(13b–c ) ] =(15a+1–13b+c ) (15a+1+13b–c ) =(15a–13b+c+1 ) (15a+13b–c+1 ) x 2 – y 2 +4+4x–1–2y =( x 2 +4x+4 ) –( y 2 +2y+1 ) = (x+2 ) 2 – (y+1 ) 2 =[(x+2 ) –(y+1 ) ] [(x+2 ) +(y+1 ) ] =(x+2–y–1 ) (x+2+y+1 ) =(x–y+1 ) (x+y+3 ) a 2 –16– x 2 +36+12a–8x =( a 2 +12a+36 ) –( x 2 +8x+16 ) = (a+6 ) 2 – (x+4 ) 2 =[(a+6 ) –(x+4 ) ] [(a+6 ) +(x+4 ) ] =(a+6–x–4 ) (a+6+x+4 ) =(a–x+2 ) (a+x+10 ) Categories: Capítulo X