CAPITULO IV
Multiplicación
Multiplicación de monomios
- Ejercicio 48
- Se suprimen los signos de agrupación más internos
- Se reduce efectuando las operaciones indicadas
- Reducimos términos semejantes
Simplificar
- x–[ 3a+2( –x+1 ) ] x–[ 3a+2( –x+1 ) ] = x–[ 3a–2x+2 ] = x–3a+2x–2 = 3x–3a–2
- –( a+b ) –3[ 2a+b( –a+2 ) ] –( a+b ) –3[ 2a+b( –a+2 ) ] = –a–b–3[ 2a–ab+2b ] = –a–b–6a+3ab–6b = –7a+3ab–7b
- –[ 3x–2y+( x–2y ) –2( x+y ) –3( 2x+1 ) ] –[ 3x–2y+( x–2y ) –2( x+y ) –3( 2x+1 ) ] = –[ 3x–2y+x–2y–2x–2y–6x–3 ] = –[ –4x–6y–3 ] = 4x+6y+3
- 4 x 2 –{ –3x+5–[ –x+x( 2–x ) ] } 4 x 2 –{ –3x+5–[ –x+x( 2–x ) ] } = 4 x 2 –{ –3x+5–[ –x+2x– x 2 ] } = 4 x 2 –{ –3x+5–x+ x 2 } = 4 x 2 –{ 5–4x+ x 2 } = 4 x 2 –5+4x– x 2 = 3 x 2 +4x–5
- 2a–{ –3x+2[ –a+3x–2( –a+b– 2+a ¯ ) ] } 2a–{ –3x+2[ –a+3x–2( –a+b– 2+a ¯ ) ] } = 2a–{ –3x+2[ –a+3x–2( –a+b–2–a ) ] } = 2a–{ –3x+2[ –a+3x–2( –2a+b–2 ) ] } = 2a–{ –3x+2[ –a+3x+4a–2b+4 ] } = 2a–{ –3x+2[ 3a+3x–2b+4 ] } = 2a–{ –3x+6a+6x–4b+8 } = 2a–{ 6a+3x–4b+8 } = 2a–6a–3x+4b–8 = –4a+4b–3x–8
- a–( x+y ) –3( x–y ) +2[ –( x–2y ) –2( –x–y ) ] a–( x+y ) –3( x–y ) +2[ –( x–2y ) –2( –x–y ) ] = a–x–y–3x+3y+2[ –x+2y+2x+2y ] = a–4x+2y+2[ x+4y ] = a–4x+2y+2x+8y = a–2x+10y
- m–( m+n ) –3{ –2m+[ –2m+n+2( –1+n ) – m+n–1 ¯ ] } m–( m+n ) –3{ –2m+[ –2m+n+2( –1+n ) – m+n–1 ¯ ] } = m – m –n–3{ –2m+[ –2m+ n –2+2n–m– n +1 ] } = –n–3{ –2m+[ –3m+2n–1 ] } = –n–3{ –2m–3m+2n–1 } = –n–3{ –5m+2n–1 } = –n+15m–6n+3 = 15m–7n+3
- –2( a–b ) –3( a+2b ) –4{ a–2b+2[ –a+b–1+2( a–b ) ] } –2( a–b ) –3( a+2b ) –4{ a–2b+2[ –a+b–1+2( a–b ) ] } = –2a+2b–3a–6b–4{ a–2b+2[ –a+b–1+2a–2b ] } = –5a–4b–4{ a–2b+2[ a–b–1 ] } = –5a–4b–4{ a–2b+2a–2b–2 } = –5a–4b–4{ 3a–4b–2 } = –5a–4b–12a+16b+8 = –17a+12b+8
- –5( x+y ) –[ 2x–y+2{ –x+y–3– x–y–1 ¯ } ] +2x –5( x+y ) –[ 2x–y+2{ –x+y–3– x–y–1 ¯ } ] +2x = –5x–5y–[ 2x–y+2{ –x+y–3–x+y+1 } ] +2x = –3x–5y–[ 2x–y+2{ –2x+2y–2 } ] = –3x–5y–[ 2x–y–4x+4y–4 ] = –3x–5y–[ –2x+3y–4 ] = –3x–5y+2x–3y+4 = –x–8y+4
- m–3( m+n ) +[ –{ –( –2m+n–2–3[ m–n+1 ] ) +m } ] m–3( m+n ) +[ –{ –( –2m+n–2–3[ m–n+1 ] ) +m } ] = m–3m–3n+[ –{ –( –2m+n–2–3m+3n–3 ) +m } ] = –2m–3n+[ –{ –( –5m+4n–5 ) +m } ] = –2m–3n+[ –{ 5m–4n+5+m } ] = –2m–3n+[ –{ 6m–4n+5 } ] = –2m–3n+[ –6m+4n–5 ] = –2m–3n–6m+4n–5 = –8m+n–5
- –3( x–2y ) +2{ –4[ –2x–3( x+y ) ] } –{ –[ –( x+y ) ] } –3( x–2y ) +2{ –4[ –2x–3( x+y ) ] } –{ –[ –( x+y ) ] } = –3x+6y+2{ –4[ –2x–3x–3y ] } –{ ( x+y ) } = –3x+6y+2{ –4[ –5x–3y ] } –x–y = –4x+5y+2{ 20x+12y } = –4x+5y+40x+24y = 36x+29y
- 5{ –( a+b ) –3[ –2a+3b–( a+b ) +( –a–b ) +2( –a+b ) ] –a } 5{ –( a+b ) –3[ –2a+3b–( a+b ) +( –a–b ) +2( –a+b ) ] –a } = 5{ –a–b–3[ –2a+3b–a– b –a– b –2a+ 2b ] –a } = 5{ –2a–b–3[ –6a+3b ] } = 5{ –2a–b+18a–9b } = 5{ 16a–10b } = 80a–50b
- –3{ –[ +( –a+b ) ] } –4{ –[ –( –a–b ) ] } –3{ –[ +( –a+b ) ] } –4{ –[ –( –a–b ) ] } = –3{ –( –a+b ) } –4{ ( –a–b ) } = –3{ a–b } +4a+4b = –3a+3b+4a+4b = a+7b
- –{ a+b–2( a–b ) +3{ –[ 2a+b–3( a+b–1 ) ] } –3[ –a+2( –1+a ) ] } –{ a+b–2( a–b ) +3{ –[ 2a+b–3( a+b–1 ) ] } –3[ –a+2( –1+a ) ] } = –{ a+b–2a+2b+3{ –[ 2a+b–3a–3b+3 ] } –3[ –a–2+2a ] } = –{ –a+3b+3{ –[ –a–2b+3 ] } –3[ –2+a ] } = –{ –a+3b+3{ a+2b–3 } +6–3a } = –{ –4a+3b+3a+6b–9+6 } = –{ –a+9b–3 } = a–9b+3