Ejercicio 62

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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES
Ejercicio 62
Escribir, por simple inspección, el resultado de:
  1. (m+3 ) 2 = m 2 +2( 3 ) ( m ) +(3 ) 2 = m 2 +6m+9
  2. (5+x ) 2 =(5 ) 2 +2( 5 ) ( x ) +(x ) 2 =25+10x+ x 2
  3. (6a+b ) 2 =(6a ) 2 +2(6a ) ( b ) +(b ) 2 =36 a 2 +12ab+ b 2
  4. (9+4m ) 2 =(9 ) 2 +2( 9 ) (4m ) +(4m ) 2 =81+72m+16 m 2
  5. (7x+11 ) 2 =(7x ) 2 +2(7x ) ( 11 ) +(11 ) 2 =49 x 2 +154x+121
  6. (x+y ) 2 =(x ) 2 +2( x ) ( y ) +(y ) 2 = x 2 +2xy+ y 2
  7. (1+3 x 2 ) 2 =(1 ) 2 +2( 1 ) (3 x 2 ) +(b ) 2 =1+6 x 2 +9 x 4
  8. (2x+3y ) 2 =(2x ) 2 +2(2x ) (3y ) +(3y ) 2 =4 x 2 +12xy+9 y 2
  9. ( a 2 x+b y 2 ) 2 =( a 2 x ) 2 +2( a 2 x ) (b y 2 ) +(b y 2 ) 2 = a 4 x+2 a 2 bx y 2 + b 2 y 4
  10. (3 a 3 +8 b 4 ) 2 =(3 a 3 ) 2 +2(3 a 3 ) (8 b 4 ) +(8 b 4 ) 2 =9 a 6 +48 a 3 b 4 +64 b 8
  11. (4 m 5 +5 n 6 ) 2 =(4 m 5 ) 2 +2(4 m 5 ) (5 n 6 ) +(5 n 6 ) 2 =16 m 10 +40 m 5 n 6 +25 n 12
  12. (7 a 2 b 3 +5 x 4 ) 2 =(7 a 2 b 3 ) 2 +2(7 a 2 b 3 ) (5 x 4 ) +(5 x 4 ) 2 =49 a 4 b 6 +70 a 2 b 3 x 4 +25 x 8
  13. (4a b 2 +5x y 3 ) 2 =(4a b 2 ) 2 +2(4a b 2 ) (5x y 3 ) +(5x y 3 ) 2 =16 a 2 b 4 +40a b 2 x y 3 +25 x 2 y 6
  14. (8 x 2 y+9 m 3 ) 2 =(8 x 2 y ) 2 +2(8 x 2 y ) (9 m 3 ) +(9 m 3 ) 2 =64 x 4 y 2 +144 m 3 x 2 y+81 m 6
  15. ( x 10 +10 y 12 ) 2 =( x 10 ) 2 +2( x 10 ) (10 y 12 ) +( x 10 ) 2 = x 20 +20 x 10 y 12 +100 y 24
  16. ( a m + a n ) 2 =( a m ) 2 +2( a m ) ( a n ) +( a n ) 2 = a 2m +2 a m+n + a 2n
  17. ( a x + b x+1 ) 2 =( a x ) 2 +2( a x ) ( b x+1 ) +( b x+1 ) 2 = a 2x +2 a x b x+1 + b 2x+2
  18. ( x a+1 + y x2 ) 2 =( x a+1 ) 2 +2( x a+1 ) ( y x2 ) +( y x2 ) 2 = x 2a+2 +2 x a+1 y x2 + y 2x4