Question

因式分解（x-2)3-(y-2)3-(x-y)3

Answer 1

会产生象前面那个回答一样的歧义.注:如果要写X的3次方:a^3-b^3=(a-b)(a^2+ab+b^2)
（x-2)^3-(y-2)^3-(x-y)^3
=[(x-2)-(y-2)][(x-2)^2+(x-2)(y-2)+(y-2)^2]-(x-y)^3
=(x-y)(x^2+y^2+xy-6x-6y+12)-(x-y)(x^2-2xy+y^2)
=(x-y)(x^2+y^2+xy-6x-6y+12-x^2+2xy-y^2)
=(x-y)(3xy-6x-6y+12)
=3(x-y)(xy-2x-2y+4)
=3(x-y)[x(y-2)-2(y-2)]
=3(x-y)(x-2)(y-2)
附.,不要写成X3

Answer 2

有一个公式的。。叫立方差公式：
a^3-b^3
=(a-b)(a^2+ab+b^2)
把（x-2)3当作a^3
把(y-2)3当作b^3
然后提取一个（x-y)就行了