Ejercicio 48

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
  1. x[3a+2(x+1 ) ] x[3a+2(x+1 ) ] = x[3a2x+2 ] = x3a+2x2 = 3x3a2
  2. (a+b ) 3[2a+b(a+2 ) ] (a+b ) 3[2a+b(a+2 ) ] = ab3[2aab+2b ] = ab6a+3ab6b = 7a+3ab7b
  3. [3x2y+(x2y ) 2(x+y ) 3(2x+1 ) ] [3x2y+(x2y ) 2(x+y ) 3(2x+1 ) ] = [3x2y+x2y2x2y6x3 ] = [4x6y3 ] = 4x+6y+3
  4. 4 x 2 {3x+5[x+x(2x ) ] } 4 x 2 {3x+5[x+x(2x ) ] } = 4 x 2 {3x+5[x+2x x 2 ] } = 4 x 2 {3x+5x+ x 2 } = 4 x 2 {54x+ x 2 } = 4 x 2 5+4x x 2 = 3 x 2 +4x5
  5. 2a{3x+2[a+3x2(a+b 2+a ¯ ) ] } 2a{3x+2[a+3x2(a+b 2+a ¯ ) ] } = 2a{3x+2[a+3x2(a+b2a ) ] } = 2a{3x+2[a+3x2(2a+b2 ) ] } = 2a{3x+2[a+3x+4a2b+4 ] } = 2a{3x+2[3a+3x2b+4 ] } = 2a{3x+6a+6x4b+8 } = 2a{6a+3x4b+8 } = 2a6a3x+4b8 = 4a+4b3x8
  6. a(x+y ) 3(xy ) +2[(x2y ) 2(xy ) ] a(x+y ) 3(xy ) +2[(x2y ) 2(xy ) ] = axy3x+3y+2[x+2y+2x+2y ] = a4x+2y+2[x+4y ] = a4x+2y+2x+8y = a2x+10y
  7. m(m+n ) 3{2m+[2m+n+2(1+n ) m+n1 ¯ ] } m(m+n ) 3{2m+[2m+n+2(1+n ) m+n1 ¯ ] } = m m n3{2m+[2m+ n 2+2nm n +1 ] } = n3{2m+[3m+2n1 ] } = n3{2m3m+2n1 } = n3{5m+2n1 } = n+15m6n+3 = 15m7n+3
  8. 2(ab ) 3(a+2b ) 4{a2b+2[a+b1+2(ab ) ] } 2(ab ) 3(a+2b ) 4{a2b+2[a+b1+2(ab ) ] } = 2a+2b3a6b4{a2b+2[a+b1+2a2b ] } = 5a4b4{a2b+2[ab1 ] } = 5a4b4{a2b+2a2b2 } = 5a4b4{3a4b2 } = 5a4b12a+16b+8 = 17a+12b+8
  9. 5(x+y ) [2xy+2{x+y3 xy1 ¯ } ] +2x 5(x+y ) [2xy+2{x+y3 xy1 ¯ } ] +2x = 5x5y[2xy+2{x+y3x+y+1 } ] +2x = 3x5y[2xy+2{2x+2y2 } ] = 3x5y[2xy4x+4y4 ] = 3x5y[2x+3y4 ] = 3x5y+2x3y+4 = x8y+4
  10. m3(m+n ) +[{(2m+n23[mn+1 ] ) +m } ] m3(m+n ) +[{(2m+n23[mn+1 ] ) +m } ] = m3m3n+[{(2m+n23m+3n3 ) +m } ] = 2m3n+[{(5m+4n5 ) +m } ] = 2m3n+[{5m4n+5+m } ] = 2m3n+[{6m4n+5 } ] = 2m3n+[6m+4n5 ] = 2m3n6m+4n5 = 8m+n5
  11. 3(x2y ) +2{4[2x3(x+y ) ] } {[(x+y ) ] } 3(x2y ) +2{4[2x3(x+y ) ] } {[(x+y ) ] } = 3x+6y+2{4[2x3x3y ] } { (x+y )} = 3x+6y+2{4[5x3y ] } xy = 4x+5y+2{20x+12y } = 4x+5y+40x+24y = 36x+29y
  12. 5{(a+b ) 3[2a+3b(a+b ) +(ab ) +2(a+b ) ] a } 5{(a+b ) 3[2a+3b(a+b ) +(ab ) +2(a+b ) ] a } = 5{ab3[2a+3ba b a b 2a+ 2b ] a } = 5{2ab3[6a+3b ] } = 5{2ab+18a9b } = 5{16a10b } = 80a50b
  13. 3{[+(a+b ) ] } 4{[(ab ) ] } 3{[+(a+b ) ] } 4{[(ab ) ] } = 3{(a+b ) } 4{ (ab )} = 3{ab } +4a+4b = 3a+3b+4a+4b = a+7b
  14. {a+b2(ab ) +3{[2a+b3(a+b1 ) ] } 3[a+2(1+a ) ] } {a+b2(ab ) +3{[2a+b3(a+b1 ) ] } 3[a+2(1+a ) ] } = {a+b2a+2b+3{[2a+b3a3b+3 ] } 3[a2+2a ] } = {a+3b+3{[a2b+3 ] } 3[2+a ] } = {a+3b+3{a+2b3 } +63a } = {4a+3b+3a+6b9+6 } = {a+9b3 } = a9b+3

Ejercicio 47

CAPITULO IV

Multiplicación
Multiplicación combinada con suma y resta
Ejercicio 47
  • Se multiplica el primer polinomio por el segundo, en cada grupo
  • Se suma ambos resultados de la multiplicacion
  • Reduciomos términos semejantes
Simplificar
  1. Mathematical Equation
  2. Mathematical Equation
  3. a(ax ) +3a(x+2a ) a(x3a ) a(ax ) +3a(x+2a ) a(x3a ) = a 2 ax+3ax+6 a 2 ax+3 a 2 = 10 a 2 +ax
  4. x 2 ( y 2 +1 ) + y 2 ( x 2 +1 ) 3 x 2 y 2 x 2 ( y 2 +1 ) + y 2 ( x 2 +1 ) 3 x 2 y 2 = x 2 y 2 + x 2 + x 2 y 2 + y 2 3 x 2 y 2 = x 2 x 2 y 2 + y 2
  5. 4 m 3 5m n 2 +3 m 2 ( m 2 + n 2 ) 3m( m 2 n 2 ) 4 m 3 5m n 2 +3 m 2 ( m 2 + n 2 ) 3m( m 2 n 2 ) = 4 m 3 5m n 2 +3 m 4 +3 m 2 n 2 3 m 3 +3m n 2 = 3 m 4 + m 3 +3 m 2 n 2 2m n 2
  6. y 2 + x 2 y 3 y 3 ( x 2 +1 ) + y 2 ( x 2 +1 ) y 2 ( x 2 1 ) y 2 + x 2 y 3 y 3 ( x 2 +1 ) + y 2 ( x 2 +1 ) y 2 ( x 2 1 ) = y 2 + x 2 y 3 x 2 y 3 y 3 + y 2 x 2 + y 2 y 2 x 2 + y 2 = y 3 +3 y 2
  7. 5(x+2 ) (x+1 ) (x+4 ) 6x 5(x+2 ) (x+1 ) (x+4 ) 6x = 5x+10( x 2 +4x+x+4 ) 6x = 5x +10 x 2 5x 46x = 66x x 2
  8. (a+5 ) (a5 ) 3(a+2 ) (a2 ) +5(a+4 ) (a+5 ) (a5 ) 3(a+2 ) (a2 ) +5(a+4 ) = a 2 5a + 5a 253( a 2 2a + 2a 4 ) +5a+20 = a 2 53 a 2 +12+5a = 7+5a2 a 2
  9. (a+b ) (4a3b ) (5a2b ) (3a+b ) (a+b ) (3a6b ) (a+b ) (4a3b ) (5a2b ) (3a+b ) (a+b ) (3a6b ) = 4 a 2 3ab+4ab3 b 2 (15 a 2 +5ab6ab2 b 2 ) (3 a 2 6ab+3ab6 b 2 ) = 4 a 2 +ab3 b 2 (15 a 2 ab2 b 2 ) (3 a 2 3ab6 b 2 ) = 4 a 2 +ab3 b 2 15 a 2 +ab+2 b 2 3 a 2 +3ab+6 b 2 = 14 a 2 +5ab+5 b 2
  10. (a+c ) 2 (ac ) 2 (a+c ) 2 (ac ) 2 = (a+c ) (a+c ) (ac ) (ac ) = a 2 +ac+ac+ c 2 ( a 2 acac+ c 2 ) = a 2 +2ac+ c 2 a 2 +2ac c 2 = 4ac
  11. 3 (x+y ) 2 4 (xy ) 2 +3 x 2 3 y 2 3 (x+y ) 2 4 (xy ) 2 +3 x 2 3 y 2 = 3( x 2 +2xy+ y 2 ) 4( x 2 2xy+ y 2 ) +3 x 2 3 y 2 = 3 x 2 +6xy+ 3 y 2 4 x 2 +8xy4 y 2 +3 x 2 3 y 2 = 2 x 2 +14xy4 y 2
  12. (m+n ) 2 (2m+n ) 2 + (m4n ) 2 (m+n ) 2 (2m+n ) 2 + (m4n ) 2 = (m+n ) (m+n ) (2m+n ) (2m+n ) +(m4n ) (m4n ) = m 2 +mn+mn+ n 2 (4 m 2 +2mn+2mn+ n 2 ) +( m 2 4mn4mn+16 n 2 ) = m 2 +2mn+ n 2 4 m 2 4mn n 2 + m 2 8mn+16 n 2 = 2 m 2 10mn+16 n 2
  13. x(a+x ) +3x(a+1 ) (x+1 ) (a+2x ) (ax ) 2 x(a+x ) +3x(a+1 ) (x+1 ) (a+2x ) (ax ) 2 = ax+ x 2 +3ax+3x(ax+2 x 2 +a+2x ) ( a 2 2ax+ x 2 ) = ax + x 2 +3ax+3x ax 2 x 2 a2x a 2 +2ax x 2 = 2 x 2 +5ax+xa a 2
  14. (a+bc ) 2 + (ab+c ) 2 (a+b+c ) 2 (a+bc ) 2 + (ab+c ) 2 (a+b+c ) 2 = (a+bc ) (a+bc ) +(ab+c ) (ab+c ) (a+b+c ) (a+b+c ) = a 2 + ab ac + ab + b 2 bc ac bc+ c 2 + a 2 ab + ac ab + b 2 bc+ ac bc+ c 2 ( a 2 +ab+ac+ab+ b 2 +bc+ac+bc+ b 2 ) = 2 a 2 +2 b 2 4bc+2 c 2 ( a 2 +2ab+2ac+2bc+ b 2 + c 2 ) = 2 a 2 +2 b 2 4bc+2 c 2 a 2 2ab2ac2bc b 2 c 2 = a 2 2ab2ac+ b 2 6bc+ c 2
  15. ( x 2 +x3 ) 2 ( x 2 2+x ) 2 + ( x 2 x3 ) 2 ( x 2 +x3 ) 2 ( x 2 2+x ) 2 + ( x 2 x3 ) 2 = ( x 2 +x3 ) ( x 2 +x3 ) ( x 2 2+x ) ( x 2 2+x ) +( x 2 x3 ) ( x 2 x3 ) = x 4 + x 3 3 x 2 + x 3 + x 2 3x3 x 2 3x+9( x 4 2 x 2 + x 3 2 x 2 +42x+ x 3 2x+ x 2 ) + x 4 x 3 3 x 2 x 3 + x 2 +3x3 x 2 +3x+9 = x 4 +2 x 3 5 x 2 6x+9( x 4 3 x 2 +2 x 3 +44x ) + x 4 2 x 3 5 x 2 +6x+9 = x 4 + 2 x 3 5 x 2 6x +9 x 4 +3 x 2 2 x 3 4+4x+ x 4 2 x 3 5 x 2 + 6x +9 = x 4 2 x 3 7 x 2 +4x+14
  16. (x+y+z ) 2 (x+y ) (xy ) +3( x 2 +xy+ y 2 ) (x+y+z ) 2 (x+y ) (xy ) +3( x 2 +xy+ y 2 ) = (x+y+z ) (x+y+z ) ( x 2 xy + xy y 2 ) +3 x 2 +3xy+3 y 2 = x 2 +xy+xz+xy+ y 2 +yz+xz+yz+ z 2 x 2 + y 2 +3 x 2 +3xy+3 y 2 = 3 x 2 +5 y 2 + z 2 +5xy+2xz+2yz
  17. [x+(2x3 ) ] [3x(x+1 ) ] +4x x 2 [x+(2x3 ) ] [3x(x+1 ) ] +4x x 2 = [x+2x3 ] [3xx1 ] +4x x 2 = [3x3 ] [2x1 ] +4x x 2 = 6 x 2 3x6x+3+4x x 2 = 5 x 2 5x+3
  18. [3(x+2 ) 4(x+1 ) ] [3(x+4 ) 2(x+2 ) ] [3(x+2 ) 4(x+1 ) ] [3(x+4 ) 2(x+2 ) ] = [3x+64x4 ] [3x+122x4 ] = [x+2 ] [x+8 ] = x 2 8x+2x+16 = x 2 6x+16
  19. [(m+n ) (mn ) (m+n ) (m+n ) ] [2(m+n ) 3(mn ) ] [(m+n ) (mn ) (m+n ) (m+n ) ] [2(m+n ) 3(mn ) ] = [ m 2 mn + mn n 2 ( m 2 +mn+mn+ n 2 ) ] [2m+2n3m+3n ] = [ m 2 n 2 m 2 2mn n 2 ] [m+5n ] = [2mn2 n 2 ] [m+5n ] = 2 m 2 n10m n 2 +2m n 2 10 n 3 = 2 m 2 n8m n 2 10 n 3
  20. [ (x+y ) 2 3 (xy ) 2 ] [(x+y ) (xy ) +x(yx ) ] [ (x+y ) 2 3 (xy ) 2 ] [(x+y ) (xy ) +x(yx ) ] = [(x+y ) (x+y ) 3(xy ) (xy ) ] [ x 2 xy + xy y 2 +xy x 2 ] = [ x 2 +xy+xy+ y 2 3( x 2 xyxy+ y 2 ) ] [ y 2 +xy ] = [ x 2 +2xy+ y 2 3 x 2 +6xy3 y 2 ] [ y 2 +xy ] = [2 x 2 +8xy2 y 2 ] [ y 2 +xy ] = 2 x 2 y 2 2 x 3 y8x y 3 +8 x 2 y 2 +2 y 4 2x y 3 = 2 x 3 y+10 x 2 y 2 10x y 3 +2 y 4