Ejercicio 32

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DESCARGA
CAPITULO III

Signos de agrupación
Supresión de signos de agrupación
Ejercicio 32
  • Se reduce los signos de agrupación más interiores
  • Cuando el signo de agrupación está precedido del signo +, no se cambian los signos de los términos, si estuviera precedido del signo – se cambiaran los términos
  • Se reducen los términos semejantes.
Simplificar, suprimiendo los signos de agrupación y reduciendo términos semejantes:
  1. 2a+[a–(a+b ) ] = 2a+[ a – a –b ] = 2a+[–b ] = 2a–b
  2. 3x–[x+y– 2x+y ¯ ] = 3x–[x+ y –2x– y ] = 3x–[–x ] = 3x+x = 4x
  3. 2m–[(m–n ) –(m+n ) ] = 2m–[ m –n– m –n ] = 2m–[–2n ] = 2m+2n
  4. 4 x 2 +[–( x 2 –xy ) +(–3 y 2 +2xy ) –(–3 x 2 + y 2 ) ] = 4 x 2 +[– x 2 +xy–3 y 2 +2xy+3 x 2 – y 2 ] = 4 x 2 +[2 x 2 +3xy–4 y 2 ] = 4 x 2 +2 x 2 +3xy–4 y 2 = 6 x 2 +3xy–4 y 2
  5. a+{(–2a+b ) –(–a+b–c ) +a } = a+{– 2a + b + a – b +c+ a } = a+{ c } = a+c
  6. 4m–[2m+ n–3 ¯ ] +[–4n– 2m+1 ¯ ] = 4m–[2m+n–3 ] +[–4n–2m–1 ] = 4m – 2m –n+3–4n– 2m –1 = –5n+2
  7. 2x+[–5x–(–2y+{–x+y } ) ] = 2x+[–5x–(–2y–x+y ) ] = 2x+[–5x+2y+x–y ] = 2x+[–4x+y ] = 2x–4x+y = –2x+y
  8. x 2 –{–7xy+[– y 2 +(– x 2 +3xy–2 y 2 ) ] } = x 2 –{–7xy+[– y 2 – x 2 +3xy–2 y 2 ] } = x 2 –{–7xy– y 2 – x 2 +3xy–2 y 2 } = x 2 +7xy+ y 2 + x 2 –3xy+2 y 2 = 2 x 2 +4xy+3 y 2
  9. –(a+b ) +[–3a+b–{–2a+b–(a–b ) } +2a ] = –a–b+[–3a+b–{–2a+b–a+b } +2a ] = –a–b+[–3a+b–{–3a+2b } +2a ] = –a–b+[– 3a +b+ 3a –2b+2a ] = –a–b+[–b+2a ] = –a–b–b+2a = a–2b
  10. (–x+y ) –{4x+2y+[–x–y– x+y ¯ ] } = –x+y–{4x+2y+[–x–y–x–y ] } = –x+y–{4x+2y+[–2x–2y ] } = –x+y–{4x+ 2y –2x– 2y } = –x+y–{2x } = –x+y–2x = –3x+y
  11. –(–a+b ) +[–(a+b ) –(–2a+3b ) +(–b+a–b ) ] = a–b+[–(a+b ) –(–2a+3b ) +(a–2b ) ] = a–b+[– a –b+2a–3b+ a –2b ] = a–b+[–6b+2a ] = a–b–6b+2a = 3a–7b
  12. 7 m 2 –{–[ m 2 +3n–(5–n ) –(–3+ m 2 ) ] } –(2n+3 ) = 7 m 2 –{–[ m 2 +3n–5+n+3– m 2 ] } –2n–3 = 7 m 2 –{–[4n–2 ] } –2n–3 = 7 m 2 –{–4n+2 } –2n–3 = 7 m 2 +4n–2–2n–3 = 7 m 2 +2n–5
  13. 2a–(–4a+b ) –{–[–4a+(b–a ) –(–b+a ) ] } = 2a+4a–b–{–[–4a+b–a+b–a ] } = 6a–b–{–[–6a+2b ] } = 6a–b–{6a–2b } = 6a –b– 6a +2b = b
  14. 3x–(5y+[–2x+{y– 6+x ¯ } –(–x+y ) ] ) = 3x–(5y+[–2x+{y– 6+x ¯ } +x–y ] ) = 3x–(5y+[–x+{y–6–x } –y ] ) = 3x–(5y+[–x+ y –6–x– y ] ) = 3x–(5y+[–2x–6 ] ) = 3x–(5y–2x–6 ) = 3x–5y+2x+6 = 5x–5y+6
  15. 6c–[–(2a+c ) +{–(a+c ) –2a– a+c ¯ } +2c ] = 6c–[–(2a+c ) +{–a–c–2a–a–c } +2c ] = 6c–[–(2a+c ) +{–4a–2c } +2c ] = 6c–[–2a–c–4a– 2c + 2c ] = 6c–[–6a–c ] = 6c+6a+c = 6a+7c
  16. –(3m+n ) –[2m+{–m+(2m– 2n–5 ¯ ) } –(n+6 ) ] = –3m–n–[2m+{–m+(2m–2n+5 ) } –n–6 ] = –3m–n–[2m+{–m+2m–2n+5 } –n–6 ] = –3m–n–[2m+{m–2n+5 } –n–6 ] = –3m–n–[2m+m–2n+5–n–6 ] = –3m–n–[3m–3n–1 ] = –3m–n–3m+3n+1 = –6m+2n+1
  17. 2a+{–[5b+(3a–c ) +2–(–a+b– c+4 ¯ ) ] –(–a+b ) } = 2a+{–[5b+3a–c+2–(–a+b–c–4 ) ] +a–b } = 2a+{–[5b+3a– c +2+a–b+ c +4 ] +a–b } = 2a+{–[4b+4a+6 ] +a–b } = 2a+{–4b–4a–6+a–b } = 2a+{–5b–3a–6 } = 2a–5b–3a–6 = –a–5b–6
  18. –[–3x+(–x– 2y–3 ¯ ) ] +{–(2x+y ) +(–x–3 ) +2– x+y ¯ } = –[–3x+(–x–2y+3 ) ] +{–2x–y–x–3+2–x–y } = –[–3x–x–2y+3 ] +{–4x–2y–1 } = –[–4x–2y+3 ] –4x–2y–1 = 4x + 2y –3– 4x – 2y –1 = –4
  19. –[–(–a ) ] –[+(–a ) ] +{–[–b+c ] –[+(–c ) ] } = –[–(–a ) ] –[+(–a ) ] +{–[–b+c ] –[+(–c ) ] } = –[ a ] –[–a ] +{b–c–[–c ] } = – a + a +{b– c + c } = b
  20. –{–[–(a+b ) ] } –{+[–(–b–a ) ] } – a+b ¯ = –{–[–a–b ] } –{+[b+a ] } –a–b = –{a+b } –{b+a } –a–b = –a–b–b–a–a–b = –3a–3b
  21. –{–[–(a+b–c ) ] } –{+[–(c–a+b ) ] } +[–{–a+(–b ) } ] = –{–[–a–b+c ] } –{+[–c+a–b ] } +[–{–a–b } ] = –{a+b–c } –{–c+a–b } +[a+b ] = – a – b +c+c–a+ b + a +b = –a+b+2c
  22. –[3m+{–m–(n– m+4 ¯ ) } +{–(m+n ) +(–2n+3 ) } ] = –[3m+{–m–(n–m–4 ) } +{–m–n–2n+3 } ] = –[3m+{–m–n+m+4 } +{–m–3n+3 } ] = –[3m– m –n+ m +4–m–3n+3 ] = –[2m–4n+7 ] = –2m+4n–7
  23. –[x+{–(x+y ) –[–x+(y–z ) –(–x+y ) ] –y } ] = –[x+{–x–y–[– x + y –z+ x – y ] –y } ] = –[x+{–x–y–[–z ] –y } ] = –[x+{–x–2y+z } ] = –[ x – x –2y+z ] = 2y–z
  24. –[–a+{–a+(a–b ) – a–b+c ¯ –[–(–a ) +b ] } ] = –[–a+{– a + a – b –a+ b –c–[a+b ] } ] = –[–a+{–a–c–a–b } ] = –[–a+{–2a–c–b } ] = –[–a–2a–c–b ] = –[–3a–c–b ] = 3a+b+c