數學知識交流 － 因式分解

= x⁹⁶ - y⁹⁶= (x⁴⁸ - y⁴⁸)(x⁴⁸ + y⁴⁸)= (x²⁴ - y²⁴)(x²⁴ + y²⁴)(x¹⁶ + y¹⁶)(x³² - x¹⁶ y¹⁶ + y³²)= (x¹² - y¹²)(x¹² + y¹²)(x⁸ + y⁸)(x¹⁶ - x⁸y⁸ + y¹⁶)(x¹⁶ + y¹⁶)(x³² - x¹⁶ y¹⁶ + y³²)= (x⁶ - y⁶)(x⁶ + y⁶)(x⁴ + y⁴)(x⁸ - x⁴y⁴ + y⁸)(x⁸ + y⁸)(x¹⁶ - x⁸y⁸ + y¹⁶)(x¹⁶ + y¹⁶)= (x³² - x¹⁶ y¹⁶ + y³²)= (x³ - y³)(x³ + y³)(x² + y²)(x⁴ - x²y² + y⁴) (x⁴ + y⁴)(x⁸ - x⁴y⁴ + y⁸)(x⁸ + y⁸)= (x¹⁶ - x⁸y⁸ + y¹⁶)(x¹⁶ + y¹⁶)(x³² - x¹⁶ y¹⁶ + y³²)= (x - y)(x² + xy +y²)(x + y)(x² - xy + y²)(x² + y²)(x⁴ - x²y² + y⁴)(x⁴ + y⁴)= (x⁸ - x⁴y⁴ + y⁸)(x⁸ + y⁸)(x¹⁶ - x⁸y⁸ + y¹⁶)(x¹⁶ + y¹⁶)(x³² - x¹⁶ y¹⁶ + y³²)= (x - y)(x + y)(x² + y²)(x² - xy +y²)(x² + xy +y²)(x⁴ + y⁴)(x⁴ - x²y² + y⁴) (x⁸ + y⁸)(x⁸ - x⁴y⁴ + y⁸)(x¹⁶ + y¹⁶)(x¹⁶ - x⁸y⁸ + y¹⁶)(x³² - x¹⁶ y¹⁶ + y³²)

x^96-y^96
=(x^48-y^48)(x^48+y^48)
=(x^24-y^24)(x^24+y^24)(x^48+y^48)
=(x^12-y^12)(x^12+y^12)(x^24+y^24)(x^48+y^48)
=(x^6-y^6)(x^6+y^6)(x^12+y^12)(x^24+y^24)(x^48+y^48)
=(x^3-y^3)(x^3+y^3)(x^6+y^6)(x^12+y^12)(x^24+y^24)(x^48+y^48)
=(x-y)(x^2+xy+y^2)(x+y)(x^2-xy+y^2)(x^6+y^6)(x^12+y^12)(x^24+y^24)(x^48+y^48)