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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES
Ejercicio 65
Escribir, por simple inspección, el resultado de:
  1. (x+y+z ) (x+yz ) =[(x+y ) +z ] [(x+y ) z ] = (x+y ) 2 ( z ) 2 = x 2 +2xy+ y 2 z 2
  2. (xy+z ) (x+yz ) =[x(yz ) ] [x+(yz ) ] = ( x ) 2 (yz ) 2 = x 2 ( y 2 2yz+ z 2 ) = x 2 y 2 +2yz z 2
  3. (x+y+z ) (xyz ) =[x+(y+z ) ] [x(y+z ) ] = ( x ) 2 (y+z ) 2 = x 2 ( y 2 +2yz+ z 2 ) = x 2 y 2 2yz z 2
  4. (m+n+1 ) (m+n1 ) =[(m+n ) +1 ] [(m+n ) 1 ] = (m+n ) 2 ( 1 ) 2 = m 2 +2m+ n 2 1
  5. (mn1 ) (mn+1 ) =[(mn ) 1 ] [(mn ) +1 ] = (mn ) 2 ( 1 ) 2 = m 2 2m+ n 2 1
  6. (x+y2 ) (xy+2 ) =[x+(y2 ) ] [x(y2 ) ] = ( x ) 2 (y2 ) 2 = x 2 ( y 2 4y+4 ) = x 2 y 2 +4y4
  7. ( n 2 +2n+1 ) ( n 2 2n1 ) =[ n 2 +(2n+1 ) ] [ n 2 (2n+1 ) ] = ( n 2 ) 2 (2n+1 ) 2 = n 4 (4 n 2 +4n+1 ) = n 4 4 n 2 4n1
  8. ( a 2 2a+3 ) ( a 2 +2a+3 ) =[( a 2 +3 ) 2a ] [( a 2 +3 ) +2a ] = ( a 2 +3 ) 2 (2a ) 2 = a 4 +6 a 2 +94 a 2 = a 4 +2 a 2 +9
  9. ( m 2 m+1 ) ( m 2 +m+1 ) =[( m 2 1 ) m ] [( m 2 1 ) +m ] = ( m 2 1 ) 2 ( m ) 2 = m 4 2 m 2 +1 m 2 = m 4 3 m 2 +1
  10. (2abc ) (2ab+c ) =[(2ab ) c ] [(2ab ) +c ] = (2ab ) 2 ( c ) 2 =4 a 2 +4ab+ b 2 c 2
  11. (2x+yz ) (2xy+z ) =[2x+(yz ) ] [2x(yz ) ] = (2x ) 2 (yz ) 2 =4 x 2 ( y 2 2yz+ z 2 ) =4 x 2 y 2 +2yz z 2
  12. ( x 2 5x+6 ) ( x 2 +5x6 ) =[ x 2 (5x6 ) ] [ x 2 +(5x6 ) ] = ( x 2 ) 2 (5x6 ) 2 = x 4 (25 x 2 60x+36 ) = x 4 25 x 2 +60x36
  13. ( a 2 ab+ b 2 ) ( a 2 + b 2 +ab ) =[( a 2 + b 2 ) ab ] [( a 2 + b 2 ) +ab ] = ( a 2 + b 2 ) 2 (ab ) 2 = a 4 +2 a 2 b 2 + b 4 a 2 b 2 = a 4 + a 2 b 2 + b 4
  14. ( x 3 x 2 x ) ( x 3 + x 2 +x ) =[ x 3 ( x 2 +x ) ] [ x 3 +( x 2 +x ) ] = ( x 3 ) 2 ( x 2 +x ) 2 = x 6 ( x 4 +2 x 3 + x 2 ) = x 6 x 4 2 x 3 x 2