(x^2-y^2)÷(x+y)=(x^3-y^3)÷(x+y)=依此类推,根据以上规律,算出(x^4-y^4)÷（x+y）=请写出具体的过程(x^3-y^3)÷(x-y)=(x-y)(x^2+xy+y^2)/(x-y)这一步是怎么得到的第2个括号里应该是x-y第2个题是(x^3-

Question

(x^2-y^2)÷(x+y)=______
(x^3-y^3)÷(x+y)=______
依此类推,根据以上规律,算出(x^4-y^4)÷（x+y）=______
请写出具体的过程
(x^3-y^3)÷(x-y)
=(x-y)(x^2+xy+y^2)/(x-y)
这一步是怎么得到的
第2个括号里应该是x-y
第2个题是(x^3-y^3)÷(x-y)=______

Answer 1

(x^2-y^2)÷(x+y)
=(x+y)(x-y)/(x+y)
=x-y;
(x^3-y^3)÷(x-y)
=(x-y)(x^2+xy+y^2)/(x-y)
=x^2+xy+y^2;
依此类推,根据以上规律,算出(x^4-y^4)÷（x+y）
=(x-y)(x+y)(x^2+y^2)/(x+y)
=(x-y)(x^2+y^2)
=x^3-x^2y+xy^2-y^3.