Ejercicio 94

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CAPITULO X

Descomposición Factorial
Ejercicio 94
Descomponer en dos factores y simplificar, si es posible:
  1. (x+y ) 2 a 2 =[(x+y ) +a ] [(x+y ) a ] =(x+y+a ) (x+ya )
  2. 4 (a+1 ) 2 =[2+(a+1 ) ] [2(a+1 ) ] =(2+a+1 ) (2a1 ) =(a+3 ) (1a )
  3. 9 (m+n ) 2 =[3+(m+n ) ] [3(m+n ) ] =(3+m+n ) (3mn )
  4. (mn ) 2 16 =[(mn ) 4 ] [(mn ) +4 ] =(mn4 ) (mn+4 )
  5. (xy ) 2 4 z 2 =[(xy ) +2z ] [(xy ) 2z ] =(xy+2z ) (xy2z )
  6. (a+2b ) 2 1 =[(a+2b ) 1 ] [(a+2b ) +1 ] =(a+2b1 ) (a+2b+1 )
  7. 1 (x2y ) 2 =[1(x2y ) ] [1+(x2y ) ] =(1x+2y ) (1+x2y )
  8. (x+2a ) 2 4 x 2 =[(x+2a ) 2x ] [(x+2a ) +2x ] =(x+2a2x ) (x+2a+2x ) =(2ax ) (2a+3x )
  9. (a+b ) 2 (c+d ) 2 =[(a+b ) +(c+d ) ] [(a+b ) (c+d ) ] =(a+b+c+d ) (a+bcd )
  10. (ab ) 2 (cd ) 2 =[(ab ) +(cd ) ] [(ab ) (cd ) ] =(ab+cd ) (abc+d )
  11. (x+1 ) 2 16 x 2 =[(x+1 ) 4x ] [(x+1 ) +4x ] =(x+14x ) (x+1+4x ) =(13x ) (5x+1 )
  12. 64 m 2 (m2n ) 2 =[8m(m2n ) ] [8m+(m2n ) ] =(8mm+2n ) (8m+m2n ) =(7m+2n ) (9m2n )
  13. (a2b ) 2 (x+y ) 2 =[(a2b ) (x+y ) ] [(a2b ) +(x+y ) ] =(a2bxy ) (a2b+x+y )
  14. (2ac ) 2 (a+c ) 2 =[(2ac ) +(a+c ) ] [(2ac ) (a+c ) ] =(2a c +a+ c ) (2acac ) =3a(a2c )
  15. (x+1 ) 2 4 x 2 =[(x+1 ) 2x ] [(x+1 ) +2x ] =(x+12x ) (x+1+2x ) =(1x ) (3x+1 )
  16. 36 x 2 (a+3x ) 2 =[6x(a+3x ) ] [6x+(a+3x ) ] =(6xa3x ) (6x+a+3x ) =(3xa ) (9x+a )
  17. a 6 (a1 ) 2 =[ a 3 (a1 ) ] [ a 3 +(a1 ) ] =( a 3 a+1 ) ( a 3 +a1 )
  18. (a1 ) 2 (m2 ) 2 =[(a1 ) (m2 ) ] [(a1 ) +(m2 ) ] =(a1m+2 ) (a1+m2 ) =(am+1 ) (a+m3 )
  19. (2x3 ) 2 (x5 ) 2 =[(2x3 ) +(x5 ) ] [(2x3 ) (x5 ) ] =(2x3+x5 ) (2x3x+5 ) =(3x8 ) (x+2 )
  20. 1 (5a+2x ) 2 =[1+(5a+2x ) ] [1(5a+2x ) ] =(1+5a+2x ) (15a2x )
  21. (7x+y ) 2 81 =[(7x+y ) 9 ] [(7x+y ) +9 ] =(7x+y9 ) (7x+y+9 )
  22. m 6 ( m 2 1 ) 2 =[ m 3 ( m 2 1 ) ] [ m 3 +( m 2 1 ) ] =( m 3 m 2 +1 ) ( m 3 + m 2 1 )
  23. 16 a 10 (2 a 2 +3 ) 2 =[4 a 5 (2 a 2 +3 ) ] [4 a 5 +(2 a 2 +3 ) ] =(4 a 5 2 a 2 3 ) (4 a 5 +2 a 2 +3 )
  24. (xy ) 2 (c+d ) 2 =[(xy ) (c+d ) ] [(xy ) +(c+d ) ] =(xycd ) (xy+c+d )
  25. (2a+bc ) 2 (a+b ) 2 =[(2a+bc ) (a+b ) ] [(2a+bc ) +(a+b ) ] =(2a+ b ca b ) (2a+bc+a+b ) =(ac ) (3a+2bc )
  26. 100 (xy+z ) 2 =[10(xy+z ) ] [10+(xy+z ) ] =(10x+yz ) (10+xy+z )
  27. x 2 (yx ) 2 =[x(yx ) ] [x+(yx ) ] =(xy+x ) ( x +y x ) =y(2xy )
  28. (2x+3 ) 2 (5x1 ) 2 =[(2x+3 ) (5x1 ) ] [(2x+3 ) +(5x1 ) ] =(2x+35x+1 ) (2x+3+5x1 ) =(43x ) (7x+2 )
  29. (xy+z ) 2 (yz+2x ) 2 =[(xy+z ) (yz+2x ) ] [(xy+z ) +(yz+2x ) ] =(xy+zy+z2x ) (xy+z+yz+2x ) =(xy+zy+z2x ) (x y + z + y z +2x ) =3x(2z2yx )
  30. (2x+1 ) 2 (x+4 ) 2 =[(2x+1 ) (x+4 ) ] [(2x+1 ) +(x+4 ) ] =(2x+1x4 ) (2x+1+x+4 ) =(x3 ) (3x+5 )
  31. (a+2x+1 ) 2 (x+a1 ) 2 =[(a+2x+1 ) (x+a1 ) ] [(a+2x+1 ) +(x+a1 ) ] =( a +2x+1x a +1 ) (a+2x+ 1 +x+a 1 ) =(x+2 ) (2a+3x )
  32. 4 (x+a ) 2 49 y 2 =[2(x+a ) 7y ] [2(x+a ) +7y ] =(2x+2a7y ) (2x+2a+7y )
  33. 25 (xy ) 2 4 (x+y ) 2 =[5(xy ) 2(x+y ) ] [5(xy ) +2(x+y ) ] =(5x5y2x2y ) (5x5y+2x+2y ) =(3x7y ) (7x3y )
  34. 36 (m+n ) 2 121 (mn ) 2 =[6(m+n ) 11(mn ) ] [6(m+n ) +11(mn ) ] =(6m+6n11m+11n ) (6m+6n+11m11n ) =(17n5m ) (17m5n )