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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 ] = 2ab
  2. 3x[x+y 2x+y ¯ ] = 3x[x+ y 2x y ] = 3x[x ] = 3x+x = 4x
  3. 2m[(mn ) (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 +xy3 y 2 +2xy+3 x 2 y 2 ] = 4 x 2 +[2 x 2 +3xy4 y 2 ] = 4 x 2 +2 x 2 +3xy4 y 2 = 6 x 2 +3xy4 y 2
  5. a+{(2a+b ) (a+bc ) +a } = a+{ 2a + b + a b +c+ a } = a+{ c } = a+c
  6. 4m[2m+ n3 ¯ ] +[4n 2m+1 ¯ ] = 4m[2m+n3 ] +[4n2m1 ] = 4m 2m n+34n 2m 1 = 5n+2
  7. 2x+[5x(2y+{x+y } ) ] = 2x+[5x(2yx+y ) ] = 2x+[5x+2y+xy ] = 2x+[4x+y ] = 2x4x+y = 2x+y
  8. x 2 {7xy+[ y 2 +( x 2 +3xy2 y 2 ) ] } = x 2 {7xy+[ y 2 x 2 +3xy2 y 2 ] } = x 2 {7xy y 2 x 2 +3xy2 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(ab ) } +2a ] = ab+[3a+b{2a+ba+b } +2a ] = ab+[3a+b{3a+2b } +2a ] = ab+[ 3a +b+ 3a 2b+2a ] = ab+[b+2a ] = abb+2a = a2b
  10. (x+y ) {4x+2y+[xy x+y ¯ ] } = x+y{4x+2y+[xyxy ] } = x+y{4x+2y+[2x2y ] } = x+y{4x+ 2y 2x 2y } = x+y{2x } = x+y2x = 3x+y
  11. (a+b ) +[(a+b ) (2a+3b ) +(b+ab ) ] = ab+[(a+b ) (2a+3b ) +(a2b ) ] = ab+[ a b+2a3b+ a 2b ] = ab+[6b+2a ] = ab6b+2a = 3a7b
  12. 7 m 2 {[ m 2 +3n(5n ) (3+ m 2 ) ] } (2n+3 ) = 7 m 2 {[ m 2 +3n5+n+3 m 2 ] } 2n3 = 7 m 2 {[4n2 ] } 2n3 = 7 m 2 {4n+2 } 2n3 = 7 m 2 +4n22n3 = 7 m 2 +2n5
  13. 2a(4a+b ) {[4a+(ba ) (b+a ) ] } = 2a+4ab{[4a+ba+ba ] } = 6ab{[6a+2b ] } = 6ab{6a2b } = 6a b 6a +2b = b
  14. 3x(5y+[2x+{y 6+x ¯ } (x+y ) ] ) = 3x(5y+[2x+{y 6+x ¯ } +xy ] ) = 3x(5y+[x+{y6x } y ] ) = 3x(5y+[x+ y 6x y ] ) = 3x(5y+[2x6 ] ) = 3x(5y2x6 ) = 3x5y+2x+6 = 5x5y+6
  15. 6c[(2a+c ) +{(a+c ) 2a a+c ¯ } +2c ] = 6c[(2a+c ) +{ac2aac } +2c ] = 6c[(2a+c ) +{4a2c } +2c ] = 6c[2ac4a 2c + 2c ] = 6c[6ac ] = 6c+6a+c = 6a+7c
  16. (3m+n ) [2m+{m+(2m 2n5 ¯ ) } (n+6 ) ] = 3mn[2m+{m+(2m2n+5 ) } n6 ] = 3mn[2m+{m+2m2n+5 } n6 ] = 3mn[2m+{m2n+5 } n6 ] = 3mn[2m+m2n+5n6 ] = 3mn[3m3n1 ] = 3mn3m+3n+1 = 6m+2n+1
  17. 2a+{[5b+(3ac ) +2(a+b c+4 ¯ ) ] (a+b ) } = 2a+{[5b+3ac+2(a+bc4 ) ] +ab } = 2a+{[5b+3a c +2+ab+ c +4 ] +ab } = 2a+{[4b+4a+6 ] +ab } = 2a+{4b4a6+ab } = 2a+{5b3a6 } = 2a5b3a6 = a5b6
  18. [3x+(x 2y3 ¯ ) ] +{(2x+y ) +(x3 ) +2 x+y ¯ } = [3x+(x2y+3 ) ] +{2xyx3+2xy } = [3xx2y+3 ] +{4x2y1 } = [4x2y+3 ] 4x2y1 = 4x + 2y 3 4x 2y 1 = 4
  19. [(a ) ] [+(a ) ] +{[b+c ] [+(c ) ] } = [(a ) ] [+(a ) ] +{[b+c ] [+(c ) ] } = [ a ] [a ] +{bc[c ] } = a + a +{b c + c } = b
  20. {[(a+b ) ] } {+[(ba ) ] } a+b ¯ = {[ab ] } {+[b+a ] } ab = {a+b } {b+a } ab = abbaab = 3a3b
  21. {[(a+bc ) ] } {+[(ca+b ) ] } +[{a+(b ) } ] = {[ab+c ] } {+[c+ab ] } +[{ab } ] = {a+bc } {c+ab } +[a+b ] = a b +c+ca+ b + a +b = a+b+2c
  22. [3m+{m(n m+4 ¯ ) } +{(m+n ) +(2n+3 ) } ] = [3m+{m(nm4 ) } +{mn2n+3 } ] = [3m+{mn+m+4 } +{m3n+3 } ] = [3m m n+ m +4m3n+3 ] = [2m4n+7 ] = 2m+4n7
  23. [x+{(x+y ) [x+(yz ) (x+y ) ] y } ] = [x+{xy[ x + y z+ x y ] y } ] = [x+{xy[z ] y } ] = [x+{x2y+z } ] = [ x x 2y+z ] = 2yz
  24. [a+{a+(ab ) ab+c ¯ [(a ) +b ] } ] = [a+{ a + a b a+ b c[a+b ] } ] = [a+{acab } ] = [a+{2acb } ] = [a2acb ] = [3acb ] = 3a+b+c