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Ejercicio 95

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DESCARGA
CAPITULO X

Descomposición Factorial
Ejercicio 95
Factorar o descomponer en dos factores:
  1. a 2 +2ab+ b 2 – x 2 = ( a+b ) 2 – x 2 =[ ( a+b ) +x ] [ ( a+b ) –x ] =( a+b+x ) ( a+b–x )
  2. x 2 –2xy+ y 2 – m 2 = ( x–y ) 2 – m 2 =[ ( x–y ) +m ] [ ( x–y ) –m ] =( x–y+m ) ( x–y–m )
  3. m 2 +2mn+ n 2 –1 = ( m+n ) 2 –1 =[ ( m+n ) –1 ] [ ( m+n ) +1 ] =( m+n–1 ) ( m+n+1 )
  4. a 2 –2a+1– b 2 = ( a–1 ) 2 – b 2 =[ ( a–1 ) +b ] [ ( a–1 ) –b ] =( a+b–1 ) ( a–b–1 )
  5. n 2 +6n+9– c 2 = ( n+3 ) 2 – c 2 =[ ( n+3 ) –c ] [ ( n+3 ) +c ] =( n–c+3 ) ( n+c+3 )
  6. 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 )
  7. 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 )
  8. 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 )
  9. 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 )
  10. 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 )
  11. 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 )
  12. 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 )
  13. 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 )
  14. 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 )
  15. 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 )
  16. 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 )
  17. 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 )
  18. 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 )
  19. 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 )
  20. 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 )
  21. 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 )
  22. 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 )
  23. – 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 )
  24. 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 )
  25. 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 )
  26. 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 )
  27. 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 )
  28. 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 )
  29. 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 )
  30. 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 )
  31. 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 )
  32. 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 )
  33. 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 )
  34. 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 )
  35. 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 )
  36. 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 )
  37. 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 )
  38. 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 )
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