(x^2-y^2)^2-8(x^2+y^2)+16因式分解如题_数学解答

(x^2-y^2)^2-8(x^2+y^2)+16因式分解
如题

人气：284 ℃　时间：2020-01-29 11:41:52

解答

(x^2-y^2)^2-8(x^2+y^2)+16
=(x^2+y^2)^2-8(x^2+y^2)+16-4x^2*y^2
=(x^2+y^2-4)^2-(2xy)^2
=(x^2+y^2+2xy-4)(x^2+y^2-2xy-4)
=[(x+y)^2-2^2][(x-y)^2-2^2]
=(x+y-2)(x+y+2)(x-y+2)(x-y-2)