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:
- 2a+[ a–( a+b ) ] = 2a+[ a – a –b ] = 2a+[ –b ] = 2a–b
- 3x–[ x+y– 2x+y ¯ ] = 3x–[ x+ y –2x– y ] = 3x–[ –x ] = 3x+x = 4x
- 2m–[ ( m–n ) –( m+n ) ] = 2m–[ m –n– m –n ] = 2m–[ –2n ] = 2m+2n
- 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
- a+{ ( –2a+b ) –( –a+b–c ) +a } = a+{ – 2a + b + a – b +c+ a } = a+{ c } = a+c
- 4m–[ 2m+ n–3 ¯ ] +[ –4n– 2m+1 ¯ ] = 4m–[ 2m+n–3 ] +[ –4n–2m–1 ] = 4m – 2m –n+3–4n– 2m –1 = –5n+2
- 2x+[ –5x–( –2y+{ –x+y } ) ] = 2x+[ –5x–( –2y–x+y ) ] = 2x+[ –5x+2y+x–y ] = 2x+[ –4x+y ] = 2x–4x+y = –2x+y
- 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
- –( 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
- ( –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
- –( –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
- 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
- 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
- 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
- 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
- –( 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
- 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
- –[ –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
- –[ –( –a ) ] –[ +( –a ) ] +{ –[ –b+c ] –[ +( –c ) ] } = –[ –( –a ) ] –[ +( –a ) ] +{ –[ –b+c ] –[ +( –c ) ] } = –[ a ] –[ –a ] +{ b–c–[ –c ] } = – a + a +{ b– c + c } = b
- –{ –[ –( 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
- –{ –[ –( 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
- –[ 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
- –[ 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
- –[ –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