1.(a-b)^2-4c(a-b)+4c^2

題目：

1.(a-b)^2-4c(a-b)+4c^2
2.(x-2y)-(2x+y)^2
3.(a-3b)^2-4c^2n
4.-2x^3n+12x^2ny^2-18x^ny^4
其中n是正整數
有解說更好
(x-2y)-(2x+y)^2
此題確實打錯了 如1L所說是.(x-2y)^2-(2x+y)^2

解答：

1.(a-b)^2-4c(a-b)+4c^2
=(a-b)^2-2*(a-b)*2c+(2c)^2
=(a-b-2c)^2
2.(x-2y)-(2x+y)^2
錯了吧
是不是(x-2y)^2-(2x+y)^2?
(x-2y)^2-(2x+y)^2
=[(x-2y)+(2x+y)][(x-2y)-(2x+y)]
=(x-2y+2x+y)(x-2y-2x-y)
=-(3x-y)(x+3y)
3.(a-3b)^2-4c^2n
=(a-3b)^2-(2c^n)^2
=(a-3b+2c^n)(a-3b-2c^n)
4.-2x^3n+12x^2ny^2-18x^ny^4
=-2x^n(x^2n-6x^ny^2+9y^4)
=-2x^n(x^n-3y^2)^2