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Unità 6 - Polinomi

Exercise

83

Scrivi il polinomio mancante al posto dei puntini in modo da ottenere uguaglianze corrette.

  1. (x+y)+(...)=3y(x+y)+(...)=3y(x+y)+(...)=3y
  2. (2x−y−z)+(...)=3x+4z(2x-y-z)+(...)=3x+4z(2x−y−z)+(...)=3x+4z
  3. (2x−y)−(...)=3x(2x-y)-(...)=3x(2x−y)−(...)=3x
  4. (3x−2y+5z)−(...)=4x−3y+7z(3x-2y+5z)-(...)=4x-3y+7z(3x−2y+5z)−(...)=4x−3y+7z

Solution

  1. (x+y)+(−x+2y)=x+y−x+2y=(x−x)+(y+2y)=3y(x+y)+(-x+2y)=x+y-x+2y=(x-x)+(y+2y)=3y(x+y)+(−x+2y)=x+y−x+2y=(x−x)+(y+2y)=3y
  2. (2x−y−z)+(x+y+5z)(2x-y-z)+(x+y+5z)(2x−y−z)+(x+y+5z) === 2x−y−z+x+y+5z2x-y-z+x+y+5z2x−y−z+x+y+5z === (2x+x)+(y−y)+(5z−z)(2x+x)+(y-y)+(5z-z)(2x+x)+(y−y)+(5z−z) === 3x+4z3x+4z3x+4z
  3. (2x−y)−(−x−y)(2x-y)-(-x-y)(2x−y)−(−x−y) === 2x−y+x+y2x-y+x+y2x−y+x+y === (2x+x)+(y−y)(2x+x)+(y-y)(2x+x)+(y−y) === 3x3x3x
  4. (3x−2y+5z)−(−x+y−2z)(3x-2y+5z)-(-x+y-2z)(3x−2y+5z)−(−x+y−2z) === 3x−2y+5z+x−y+2z3x-2y+5z+x-y+2z3x−2y+5z+x−y+2z === (3x+x)+(−2y−y)+(5z+2z)(3x+x)+(-2y-y)+(5z+2z)(3x+x)+(−2y−y)+(5z+2z) === 4x−3y+7z4x-3y+7z4x−3y+7z

Altri Esercizi

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