(x+y)( )=x^4-y^4

2026年09月27日 10:45
有3个网友回答
网友(1):

x^4-y^4=(x^2+y^2)*(x^2-y^2)
=(x^2+y^2)*(x+y)*(x-y)
=(x+y)*(x^2+y^2)*(x-y)
=(x+y)*(x^3+xy^2-x^2y-y^3)

所以应该填 (x^3+xy^2-x^2y-y^3)

网友(2):

x^4-y^4=(x^2+y^2)(x^2-y^2)=(x^2+y^2)(x-y)(x+y)=(x+y)(x^3-x^2y+xy^2-y^3)
(x+y)(x^3-x^2y+xy^2-y^3)=x^4-y^4

网友(3):

(x+y)(x-y)(x²+y²)=x^4-y^4