x^2-x+1/4-y^2（因式分解）(x^2-2xy)^2+2y^2(x^2-2xy)+y^4（因式分解）（x+y)^2(x-y)^2（计算）(2x+3y-4z)(2x-3y+4z)（计算）今天一定要告诉我啊,

Question

x^2-x+1/4-y^2（因式分解）
(x^2-2xy)^2+2y^2(x^2-2xy)+y^4（因式分解）
（x+y)^2(x-y)^2（计算）
(2x+3y-4z)(2x-3y+4z)（计算）今天一定要告诉我啊,

Answer 1

x^2-x+1/4-y^2
=(x-1/2)^2-y^2
=(x+y-1/2)(x-y-1/2)
(x^2-2xy)^2+2y^2(x^2-2xy)+y^4
=(x^2-2xy+y^2)^2
=(x-y)^4
（x+y)^2(x-y)^2
=(x^2-y^2)^2
=x^4-2x^2y^2+y^4
(2x+3y-4z)(2x-3y+4z)
=(2x)^2-(3y-4z)^2
=4x^2-9y^2+24yz-16z^2