(x+2y)^2(x-2y)^2-(2x+y)^2(2x-y)^2

因式分解
2024-11-18 10:36:44
推荐回答(2个)
回答1:

(x+2y)^2(x-2y)^2-(2x+y)^2(2x-y)^2
=(x^2-4y^2)^2-(4x^2-y^2)^2
=(x^2-4y^2+4x^2-y^2)(x^2-4y^2-4x^2+y^2)
=-(5x^2-5y^2)(3x^2+3y^2)
=-15(x^2-y^2)(x^2+y^2)
=-15(x-y)(x+y)(x^2+y^2)

回答2:

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