Respuestas
Respuesta: (35/216)x³ - (1/24)x²y + (5/12)xy² - (19/216)y³.
Explicación paso a paso: Tenemos que:
[ (x/2) + (y/3) ]³ = (x/2)³ + 3 (x/2)²(y/3) + 3(x/2)(y/3)² + (y/3)³
= x³ / 8 + 3x²y / 24 + 3xy² / 18 + y³ / 27
= x³ / 8 + x²y / 8 + xy² / 6 + y³ / 27
[ (x/3) - (y/2) ]³ = (x/3)³ - 3 (x/3)² (y/2) + 3(x/3)(y/2)² - (y/2)³
= x³ / 27 - 3x²y / 18 + 3xy² / 12 - y³ / 8
= x³ / 27 - x²y / 6 + xy² / 4 - y³ / 8
Por tanto:
[ (x/2) + (y/3) ]³ + [ (x/3) - (y/2) ]³
= x³ / 8 + x²y / 8 + xy² / 6 + y³ / 27 + x³ / 27 - x²y / 6 + xy² / 4 - y³ / 8
= (1/8 + 1/27)x³ + (1/8 - 1/6)x²y + (1/6 + 1/4)xy² + (1/27 - 1/8)y³
= (35/216)x³ + (-1/24)x²y + (5/12)xy² + (-19/216)y³
= (35/216)x³ - (1/24)x²y + (5/12)xy² - (19/216)y³