Question

x的六次方减y的六次方等于多少?

Answer 1

解法1：
x^6-y^6
=(x^3)^2-(y^3)^2
=(x^3 +y^3)(x^3 - y^3)
=(x+y)(x^2 - xy + y^2)(x - y)(x^2 + xy + y^2)

解法2：
x^6-y^6
=(x^2-y^2)(x^4+y^4+x^2y^2)

=(x+y)(x-y)(x^4 + y^4 + 2x^2y^2 - x^2y^2)
=(x+y)(x-y)[(x^2+y^2)^2 - (xy)^2]
=(x+y)(x-y)(x^2 + xy + y^2)(x^2 - xy + y^2)

解法3：
因式定理法
当x=y时，原式为0；
当x=-y时，原式为0；
所以x^6-y^6中有因式(x-y)(x+y),用多项式除法得到
x^6-y^6 = (x+y)(x-y)(x^4+y^4+x^2y^2)
=(x+y)(x-y)(x^4 + y^4 + 2x^2y^2 - x^2y^2)
=(x+y)(x-y)[(x^2+y^2)^2 - (xy)^2]
=(x+y)(x-y)(x^2 + xy + y^2)(x^2 - xy + y^2)。
希望我的方法能帮助到你，呵呵~

Answer 2

x^6-y^6
=(x^2-y^2)(x^4-y^4+x^2y^2)
=(x+y)(x-y)[(x^2+y^2)(x+y)(x-y)+x^2y^2]
=x^2y^2(x+y)^2(x-y)^2

Answer 3