Ejercicio 68

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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES
Ejercicio 68
Miscelanea
Escribir, por simple inspección, el resultado de:
  1. (x+2 ) 2 = ( x ) 2 +2( x ) ( 2 ) + ( 2 ) 2 = x 2 +4x+4
  2. (x+2 ) (x+3 ) = ( x ) 2 +(2+3 ) ( x ) +(2 × 3 ) = x 2 +5x+6
  3. (x+1 ) (x1 ) = ( x ) 2 ( 1 ) 2 = x 2 1
  4. (x1 ) 2 = ( x ) 2 2( x ) ( 1 ) + ( 1 ) 2 = x 2 2x+1
  5. (n+3 ) (n+5 ) = ( n ) 2 +(3+5 ) ( n ) +[3 × 5 ] = n 2 +8n+15
  6. (m3 ) (m+3 ) = ( m ) 2 ( 3 ) 2 = m 2 9
  7. (a+b+1 ) (a+b1 ) =[(a+b ) +1 ] [(a+b ) 1 ] = (a+b ) 2 ( 1 ) 2 = a 2 +2ab+ b 2 1
  8. (1+b ) 3 = ( 1 ) 3 +3 ( 1 ) 2 ( b ) +3( 1 ) ( b ) 2 + ( b ) 3 =1+3b+3 b 2 + b 3
  9. ( a 2 +4 ) ( a 2 4 ) = ( a 2 ) 2 ( 4 ) 2 = a 4 16
  10. (3ab5 x 2 ) 2 = (3ab ) 2 2(3ab ) (5 x 2 ) + (5 x 2 ) 2 =9 a 2 b 2 30ab x 2 +25 x 4
  11. (ab+3 ) (3ab ) =(3+ab ) (3ab ) = ( 3 ) 2 (ab ) 2 =9 a 2 b 2
  12. (14ax ) 2 = ( 1 ) 2 +2( 1 ) (4ax ) + (4ax ) 2 =18ax+16 a 2 x 2
  13. ( a 2 +8 ) ( a 2 7 ) = ( a 2 ) 2 +(87 ) ( a 2 ) +[8(7 ) ] = a 4 + a 2 56
  14. (x+y+1 ) (xy1 ) =[x+(y+1 ) ] [x(y+1 ) ] = ( x ) 2 (y+1 ) 2 = x 2 ( y 2 +2y+1 ) = x 2 y 2 2y1
  15. (1a ) (a+1 ) =(1a ) (1+a ) =1 a 2
  16. (m8 ) (m+12 ) = ( m ) 2 +(8+12 ) ( m ) +[(8 ) × 12 ] = m 2 +4m96
  17. ( x 2 1 ) ( x 2 +3 ) = ( x 2 ) 2 +(1+3 ) ( x 2 ) +[(1 ) × 3 ] = x 4 +2 x 2 3
  18. ( x 3 +6 ) ( x 3 8 ) = ( x 3 ) 2 +(68 ) ( x 3 ) +[6(8 ) ] = x 6 2 x 3 48
  19. (5 x 3 +6 m 4 ) 2 = (5 x 3 ) 2 +2(5 x 3 ) (6 m 4 ) + (6 m 4 ) 2 =25 x 6 +60 x 3 m 4 +36 m 8
  20. ( x 4 2 ) ( x 4 +5 ) = ( x 4 ) 2 +(2+5 ) ( x 4 ) +[(2 ) × 5 ] = x 8 +3 x 4 10
  21. (1a+b ) (ba1 ) =[(ba ) +1 ] [(ba ) 1 ] = (ba ) 2 ( 1 ) 2 = b 2 2ab+ a 2 1
  22. ( a x + b n ) ( a x b n ) = ( a x ) 2 ( b n ) 2 = a 2x b 2n
  23. ( x a+1 8 ) ( x a+1 +9 ) = ( x a+1 ) 2 +(8+9 ) ( x a+1 ) +[(8 ) × 9 ] = x 2a+2 + x a+1 72
  24. ( a 2 b 2 + c 2 ) ( a 2 b 2 c 2 ) = ( a 2 b 2 ) 2 ( c 2 ) 2 = a 4 b 2 c 4
  25. (2a+x ) 3 = (2a ) 3 +3 (2a ) 2 ( x ) +3(2a ) ( x ) 2 + ( x ) 3 =8 a 3 +12 a 2 x+6a x 2 + x 3
  26. ( x 2 11 ) ( x 2 2 ) = ( x 2 ) 2 +(112 ) ( x 2 ) +[(11 ) (2 ) ] = x 4 13 x 2 +22
  27. (2 a 3 5 b 4 ) 2 = (2 a 3 ) 2 +2(2 a 3 ) (5 b 4 ) + (5 b 4 ) 2 =4 a 6 20 a 3 b 4 +25 b 8
  28. ( a 3 +12 ) ( a 3 15 ) = ( a 3 ) 2 +(1215 ) ( a 3 ) +[12(15 ) ] = a 6 3 a 3 180
  29. ( m 2 m+n ) (n+m+ m 2 ) =[( m 2 +n ) m ] [( m 2 +n ) +m ] = ( m 2 +n ) 2 ( m ) 2 = m 4 +2mn+ n 2 m 2
  30. ( x 4 +7 ) ( x 4 11 ) = ( x 4 ) 2 +(711 ) ( x 4 ) +[7(11 ) ] = x 8 4 x 4 77
  31. (11ab ) 2 = ( 11 ) 2 +2( 11 ) (ab ) + (ab ) 2 =12122ab+ a 2 b 2
  32. ( x 2 y 3 8 ) ( x 2 y 3 +6 ) = ( x 2 y 3 ) 2 +(8+6 ) ( x 2 y 3 ) +[(8 ) × 6 ] = x 4 y 6 2 x 2 y 3 48
  33. (a+b ) (ab ) ( a 2 b 2 ) =( a 2 b 2 ) ( a 2 b 2 ) = ( a 2 b 2 ) 2 = ( a 2 ) 2 2( a 2 ) ( b 2 ) + ( b 2 ) 2 = a 4 2 a 2 b 2 + b 4
  34. (x+1 ) (x1 ) ( x 2 2 ) =( x 2 1 ) ( x 2 2 ) = ( x 2 ) 2 +(12 ) ( x 2 ) +[(1 ) (2 ) ] = x 4 3 x 2 +2
  35. (a+3 ) ( a 2 +9 ) (a3 ) =( a 2 9 ) ( a 2 +9 ) = ( a 2 ) 2 ( 9 ) 2 = a 4 81
  36. (x+5 ) (x5 ) ( x 2 +1 ) =( x 2 25 ) ( x 2 +1 ) = ( x 2 ) 2 +(25+1 ) ( x 2 ) +[(25 ) × 1 ] = x 4 24x25
  37. (a+1 ) (a1 ) (a+2 ) (a2 ) =( a 2 1 ) ( a 2 4 ) = ( a 2 ) 2 +(14 ) ( a 2 ) +[(1 ) (4 ) ] = a 4 5 a 2 +4
  38. (a+2 ) (a3 ) (a2 ) (a+3 ) =( a 2 4 ) ( a 2 9 ) = ( a 2 ) 2 +(49 ) ( a 2 ) +[(4 ) (9 ) ] = a 4 13 a 2 +36