Question

两道公因式题 求解

X的三次方+X-Y的三次方-Y X的三次方-X的二次方-Y的三次方+Y的二次方
有知道的麻烦解析下哈 最好有步骤 谢谢了

Answer 1

x^3+x-y^3-y
=(x^3-y^3)+(x-y)
=(x-y)(x^2+xy+y^2)+(x-y)
=(x-y)(x^2+xy+y^2+1).

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

Answer 2

x³+x-y³-y
=(x³-y³)+(x-y)
=(x-y)(x²+xy+y²)+(x-y)
=(x-y)(x²+xy+y²+1)

x³+x²-y³-y²
=(x³-y³)+(x²-y²)
=(x-y)(x²+xy+y²)+(x+y)(x-y)
=(x-y)(x²+xy+y²+x+y)

Answer 3

x³+x--y³--y=x³--y³+x--y=（x--y）（x²+xy+y²）+x--y=（x--y）（x²+xy+y²+1）
x³--x²--y³+y²=（x--y）（x²+xy+y²）--（x--y）（x+y）==（x--y）（x²+xy+y²--x--y）