(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4

来源：学生作业帮助网编辑：作业帮时间：2024/05/03 14:03:11

(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4
(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4

(x+2y)^4-3(x^2-4y^2)^4-18(2y-x)^4
(x+2y)^4-3(x²-4y²)²-18(2y-x)^4
=(x+2y)^4-3(x²-4y²)²-18(x-2y)^4
=(x+2y)^4-3(x+2y)²(x-2y)²-18(x-2y)^4
=[(x+2y)²+3(x-2y)²)][(x+2y)²-6(x-2y)²]
=(x²+4xy+y²+3x²-12xy+12y²)(x²+4xy+y²-6x²+24xy-24y²)
=(4x²-8xy+13y²)(-5x²+28xy-23y²)
=-(4x²-8xy+13y²)(5x²-28xy+23y²)
=-(4x²-8xy+13y²)(x-y)(5x-23y)