Ejercicio 228

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CAPITULO XXX

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Ejercicio 228
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  1. ( a 1 2 + b 1 2 ) 2 = ( a 1 2 ) 2 +2 a 1 2 b 1 2 + ( b 1 2 ) 2 =a+2 a 1 2 b 1 2 +b
  2. ( x 3 4 y 1 3 ) 2 = ( x 3 ) 2 2 x 3 4 y 1 3 + ( y 1 3 ) 2 = x 3 2 2 x 3 4 y 1 3 + y 2 3
  3. ( m 1 2 +2m ) 2 = ( m 1 2 ) 2 +2.2 m 1 2 +1 + (2m ) 2 = m 1 +4 m 1 2 +4 m 2
  4. ( a 2 b 3 a 3 b 2 ) 2 = ( a 2 b 3 ) 2 2 a 2+3 b 32 + ( a 3 b 2 ) 2 = a 4 b 6 2ab+ a 6 b 4
  5. ( a 1 3 b 3 4 ) 2 = ( a 1 ) 2 2.3 a 1 b 3 4 + (3 b 3 ) 2 = a 2 6 a 1 b 3 4 +9 b 3 2
  6. ( a 2 + b ) 2 = ( a 2 ) 2 +2 a 2 b + (b ) 2 = a 4 +2 a 2 b +b
  7. ( x 3 4 y 1 2 ) 2 = ( x 3 ) 2 2 x 3 4 y 1 2 + ( y 1 2 ) 2 = x 3 2 x 3 4 y 1 2 + y 1
  8. ( m 2 n 1 4 m 1 2 n 1 ) 2 = ( m 2 n 1 4 ) 2 m 2+ 1 2 n 1 4 1 + ( m 1 2 n 1 ) 2 = m 4 n 1 2 m 3 2 n 3 4 +m n 2
  9. ( a 1 3 + b 1 3 ) 3 = ( a 1 3 ) 3 +3 ( a 1 3 ) 2 b 1 3 +3 a 1 3 ( b 1 3 ) 2 + ( b 1 3 ) 3 =a+3 a 2 3 b 1 3 +3 a 1 3 b 2 3 +b
  10. ( x 2 3 3 y 1 ) 3 = ( x 2 3 ) 3 3 ( x 2 3 ) 2 (3 y 1 ) +3 x 2 3 (3 y 1 ) 2 (3 y 1 ) 3 = x 2 9 x 4 3 y 1 +3 x 2 3 .9 y 2 3 3 y 3 = x 2 9 x 4 3 y 1 +27 x 2 3 y 2 27 y 3
  11. ( m 2 3 +4 n 3 2 ) 3 = ( m 2 3 ) 3 +3 ( m 2 3 ) 2 (4 n 3 2 ) +3 m 2 3 (4 n 3 2 ) 2 + (4 n 3 2 ) 3 = m 2 +12 m 4 3 n 3 2 +3 m 2 3 4 2 n 3 + 4 3 n 9 2 = m 2 +12 m 4 3 n 3 2 +48 m 2 3 n 3 +64 n 9 2
  12. (2 a 4 3 b 1 2 ) 3 = (2 a 4 ) 3 3 (2 a 4 ) 2 (3 b 1 2 ) +3(2 a 4 ) (3 b 1 2 ) 2 (3 b 1 2 ) 3 = 2 3 a 12 3 2 . 2 2 a 8 b 1 2 + 3 3 .2 a 4 b 1 3 3 b 3 2 =8 a 12 36 a 8 b 1 2 +54 a 4 b 1 27 b 3 2
  13. ( x y3 ) 3 = ( x 1 2 ) 3 3 ( x 1 2 ) 2 y 1 3 +3 x 1 2 ( y 1 3 ) 2 ( y 1 3 ) 3 = x 3 2 3x y 1 3 +3 x 1 2 y 2 3 y
  14. ( a 1 2 + b 2 3 ) 4 = ( a 1 2 ) 4 +4 ( a 1 2 ) 3 ( b 2 3 ) +6 ( a 1 2 ) 2 ( b 2 3 ) 2 +4( a 1 2 ) ( b 2 3 ) 3 + ( b 2 3 ) 4 = a 2 +4 a 3 2 b 2 3 +6a b 4 3 +4 a 1 2 b 2 + b 8 3
  15. ( x 2 y 1 3 ) 4 = ( x 2 ) 4 4 ( x 2 ) 3 ( y 1 3 ) +6 ( x 2 ) 2 ( y 1 3 ) 2 4( x 2 ) ( y 1 3 ) 3 + ( y 1 3 ) 4 = x 8 4 x 6 y 1 3 +6 x 4 y 2 3 4 x 2 y 1 + y 4 3
  16. ( x 1 3 + y 3 4 ) 5 = ( x 1 3 ) 5 +5 ( x 1 3 ) 4 ( y 3 4 ) +10 ( x 1 3 ) 3 ( y 3 4 ) 2 +10 ( x 1 3 ) 2 ( y 3 4 ) 3 +5( x 1 3 ) ( y 3 4 ) 4 + ( y 3 4 ) 5 = x 5 3 +5 x 4 3 y 3 4 +10x y 3 2 +10 x 2 3 y 9 4 +5 x 1 3 y 3 + y 15 4
  17. ( m n3 ) 5 = ( m 1 2 ) 5 5 ( m 1 2 ) 4 ( n 1 3 ) +10 ( m 1 2 ) 3 ( n 1 3 ) 2 10 ( m 1 2 ) 2 ( n 1 3 ) 3 +5( m 1 2 ) ( n 1 3 ) 4 ( n 1 3 ) 5 = m 5 2 5 m 2 n 1 3 +10 m 3 2 n 2 3 10mn+5 m 1 2 n 4 3 n 5 3
  18. ( a 2 2 m ) 6 = ( a 2 ) 6 6 ( a 2 ) 5 (2 m 1 2 ) +15 ( a 2 ) 4 (2 m 1 2 ) 2 20 ( a 2 ) 3 (2 m 1 2 ) 3 +15 ( a 2 ) 2 (2 m 1 2 ) 4 6( a 2 ) (2 m 1 2 ) 5 + (2 m 1 2 ) 6 = a 12 12 a 10 m 1 2 +15. 2 2 a 8 m20. 2 3 a 6 m 3 2 +15. 2 4 a 4 m 2 6. 2 5 a 2 m 5 2 + 2 6 m 3 = a 12 12 a 10 m 1 2 +60 a 8 m160 a 6 m 3 2 +240 a 4 m 2 192 a 2 m 5 2 +64 m 3
  19. ( x 3 + y4 ) 5 = ( x 3 ) 5 +5 ( x 3 ) 4 ( y 1 4 ) +10 ( x 3 ) 3 ( y 1 4 ) 2 +10 ( x 3 ) 2 ( y 1 4 ) 3 +5( x 3 ) ( y 1 4 ) 4 + ( y 1 4 ) 5 = x 15 +5 x 12 y 1 4 +10 x 9 y 1 2 +10 x 6 y 3 4 +5 x 3 y+ y 5 4
  20. ( a 2 +3 a 1 +2 ) 2 = ( a 2 ) 2 + (3 a 1 ) 2 + 2 2 +2( a 2 ) (3 a 1 ) +2( a 2 ) ( 2 ) +2(3 a 1 ) ( 2 ) = a 4 +9 a 2 +4+6 a 3 +4 a 2 +12 a 1
  21. ( x 1 2 x 1 4 +2 x 1 4 ) 2 = ( x 1 2 ) 2 + ( x 1 4 ) 2 + (2 x 1 4 ) 2 +2( x 1 2 ) ( x 1 4 ) +2( x 1 2 ) (2 x 1 4 ) +2( x 1 4 ) (2 x 1 4 ) =x+ x 1 2 + 2 2 x 1 2 2 x 1 2 + 1 4 + 2 2 x 1 2 1 4 2 2 x 1 4 1 4 =x+ x 1 2 +4 x 1 2 2 x 3 4 +4 x 1 4 4
  22. ( a 1 2 +3+ a 1 2 ) 2 = ( a 1 2 ) 2 + ( 3 ) 2 + ( a 1 2 ) 2 +2( a 1 2 ) ( 3 ) +2( a 1 2 ) ( a 1 2 ) +2( 3 ) ( a 1 2 ) = a 1 +9+a+6 a 1 2 +2 a 1 2 + 1 2 +6 a 1 2 = a 1 +9+a+6 a 1 2 +2+6 a 1 2 = a 1 +6 a 1 2 +11+a+6 a 1 2
  23. (m+2 m 3 4 3 m 1 2 ) 2 = m 2 + (2 m 3 4 ) 2 + (3 m 1 2 ) 2 +2m(2 m 3 4 ) +2m(3 m 1 2 ) +2(2 m 3 4 ) (3 m 1 2 ) = m 2 + 2 2 m 3 2 + (3 ) 2 m+ 2 2 m 1+ 3 4 6 m 1+ 1 2 2 2 .3 m 3 4 + 1 2 = m 2 +4 m 3 2 +9m+4 m 7 4 6 m 3 2 12 m 5 4 = m 2 +4 m 7 4 2 m 3 2 12 m 5 4 +9m
  24. ( a 1 2 b 1 3 2+ a 1 2 b 1 3 ) 2 = ( a 1 2 b 1 3 ) 2 + (2 ) 2 + ( a 1 2 b 1 3 ) 2 +2( a 1 2 b 1 3 ) (2 ) +2( a 1 2 b 1 3 ) ( a 1 2 b 1 3 ) +2(2 ) ( a 1 2 b 1 3 ) =a b 2 3 +4+ a 1 b 2 3 4 a 1 2 b 1 3 +2 a 1 2 1 2 b 1 3 + 1 3 4 a 1 2 b 1 3 =a b 2 3 +4+ a 1 b 2 3 4 a 1 2 b 1 3 +24 a 1 2 b 1 3 = a 1 b 2 3 4 a 1 2 b 1 3 +64 a 1 2 b 1 3 +a b 2 3
  25. ( x 1 2 + x 1 4 1 ) 3 = ( x 1 2 ) 3 + ( x 1 4 ) 3 + (1 ) 3 +3 ( x 1 2 ) 2 ( x 1 4 ) +3 ( x 1 2 ) 2 (1 ) +3 ( x 1 4 ) 2 ( x 1 2 ) +3 ( x 1 4 ) 2 (1 ) +3 (1 ) 2 ( x 1 4 ) +3 (1 ) 2 ( x 1 2 ) +6(1 ) ( x 1 4 ) ( x 1 2 ) = x 3 2 + x 3 4 1+3x x 1 4 3x+3 x 1 2 x 1 2 3 x 1 2 +3 x 1 4 + 3 x 1 2 6 x 1 4 x 1 2 = x 3 2 + x 3 4 1+3 x 5 4 3x + 3x +3 x 1 4 6 x 3 4 = x 3 2 +3 x 5 4 5 x 3 4 +3 x 1 4 1
  26. ( a 2 3 2+ a 2 3 ) 3 = ( a 2 3 ) 3 + (2 ) 3 + ( a 2 3 ) 3 +3 ( a 2 3 ) 2 (2 ) +3 ( a 2 3 ) 2 ( a 2 3 ) +3 (2 ) 2 ( a 2 3 ) +3 (2 ) 2 ( a 2 3 ) +3 ( a 2 3 ) 2 ( a 2 3 ) +3 ( a 2 3 ) 2 (2 ) +6( a 2 3 ) (2 ) ( a 2 3 ) = a 2 8+ a 2 6 a 4 3 +3 a 4 3 a 2 3 +3.4 a 2 3 +3.4 a 2 3 +3 a 4 3 a 2 3 6 a 4 3 12 a 2 3 a 2 3 = a 2 8+ a 2 6 a 4 3 +3 a 2 3 +12 a 2 3 +12 a 2 3 +3 a 2 3 6 a 4 3 12 = a 2 6 a 4 3 +15 a 2 3 20+15 a 2 3 6 a 4 3 + a 2
  27. ( m 1 6 +2 m 1 3 + m 1 2 ) 3 = ( m 1 6 ) 3 + (2 m 1 3 ) 3 + ( m 1 2 ) 3 +3 ( m 1 6 ) 2 (2 m 1 3 ) +3 ( m 1 6 ) 2 ( m 1 2 ) +3 (2 m 1 3 ) 2 ( m 1 6 ) +3 (2 m 1 3 ) 2 ( m 1 2 ) +3 ( m 1 2 ) 2 ( m 1 6 ) +3 ( m 1 2 ) 2 (2 m 1 3 ) +6 m 1 6 (2 m 1 3 ) ( m 1 2 ) = m 1 2 + 2 3 m+ m 3 2 +6 m 1 3 m 1 3 +3 m 1 3 m 1 2 +3. 2 2 m 2 3 m 1 6 +3. 2 2 m 2 3 m 1 2 +3m m 1 6 +6m m 1 3 +12 m 1 6 m 1 3 m 1 2 = m 1 2 +8m+ m 3 2 +6 m 2 3 +3 m 5 6 +12 m 5 6 +12 m 7 6 +3 m 7 6 +6 m 4 3 +12m = m 3 2 +6 m 4 3 +15 m 7 6 +20m+15 m 5 6 +6 m 2 3 + m 1 2