分解因式 (1)x三次方+x²y-xy²-y三次方(2)a²-a(3)x四次方-1(4)(x+2)(x+4)+x²-4

题目

分解因式 (1)x三次方+x²y-xy²-y三次方(2)a²-a(3)x四次方-1(4)(x+2)(x+4)+x²-4
最好有过程哦 谢谢

答案

(1)x三次方+x²y-xy²-y三次方
=x²(x+y)-y²(x+y)
=(x+y)(x²-y²)
=(x+y)²(x-y)
(2)a²-a=a(a-1)
(3)x四次方-1
=(x²+1)(x²-1)
=(x²+1)(x+1)(x-1)
(4)(x+2)(x+4)+x²-4
=(x+2)(x+4)+(x+2)(x-2)
=(x+2)(x+4+x-2)
=2(x+2)