求解一道高中因式分解：X^24-y^24 (要详细过程)

Question

如题，X^24-Y^24
速度求解，高手来，要详细过程。

Answer 1

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

你俩咋不一样。。。哪个对。。

追答

=(x^12+y^12)(x^6+y^6)(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x^4+y^4)(x^8-x^4y^4+y^8)(x^2+y^2)(x^4-x^2y^2+y^4)(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
忘了写完了。。。

Answer 2

（x12-y12）(x12+y12)=(x6-y6)(x6+y6)(x12+y12)=(x3-y3)(x3+y3)(X6+Y6)(X12+Y12)
=(X-Y)(x2+xy+y2)(x+y)(x2-xy+y2)(x2+y2)(x4-x2y2+y4)(x3+y3)(x6-x3y3+y6)=(x-y)(x2+xy+y2)(x+y)2(x2-xy+y2)2(x2+y2)(x4-x2y2+y4)(x5-x3y3+y6)追问

你俩咋不一样。。。哪个对。。

追答

他的，我把4写成3了汗....

Answer 3

解：主要是利用立方和公式，立方差公式和平方差公式
X^24-Y^24
=(X^12+Y^12)(X^12-Y^12)
=(X^4+Y^4)(X^8-X^4Y^4+Y^8)(X^6+Y^6)(X^6-Y^6)
=(X^4+Y^4)(X^8-X^4Y^4+Y^8)(X^2+Y^2)(X^4-X^2Y^2+Y^4)(X^3+Y^3)(X^3-Y^3)
=(X^4+Y^4)(X^8-X^4Y^4+Y^8)(X^2+Y^2)(X^4-X^2Y^2+Y^4)(X+Y)(X^2-XY+Y^2)(X-Y)(X^2+xy+y^2)