Question

(x+y)*(x^2-xy+y^2)-(x-y)*x^2+xy+y^2)

Answer 1

方法一：(x+y)*(x^2-xy+y^2)-(x-y)*x^2+xy+y^2)
=(x+y)*[(x^2+y^2)-xy]-(x-y)[(x^2+y^2)+xy]
=x*(x^2+y^2)-x^2y+y(x^2+y^2)-xy^2-x(x^2+y^2)-x^2y+y(x^2+y^2)+xy^2
=x*(x^2+y^2)-x*(x^2+y^2)-x^2y-x^2y+y*(x^2+y^2)+y*(x^2+y^2)-xy^2+xy^2
=-2x^2y+2y*(x^2+y^2)
=-2x^2y+2yx^2+2y^3
=2y^3
方法二
利用a^3+b^3=(a+b)(a^2-ab+b^2) a^3-b^3=(a-b)(a^2+ab-b^2)
所以(x+y)*(x^2-xy+y^2)=（x+y）^3
(x-y)*x^2+xy+y^2)=(x-y)^3
(x+y)*(x^2-xy+y^2)-(x-y)*（x^2+xy+y^2)
=(x^3+y^3)-(x^3-y^3)
=2y^3

Answer 2

(x+y)*(x^2-xy+y^2)-(x-y)*x^2+xy+y^2)
解：
(x+y)*(x^2-xy+y^2)-(x-y)*x^2+xy+y^2)
=x³+y³-(x³-y³)
=x³+y³-x³+y³
=2y³

Answer 3

(x+y)*(x^2-xy+y^2)-(x-y)*x^2+xy+y^2)
=x^3+y^3-x^3-x^2y-xy^2+x^2y+xy^2+y^3
=2y^3
o(∩_∩)o