Đáp án + Giải thích các bước giải:
`A=x^4+2x^3z-2xz^3-z^4-4x^2y^2+4y^2z^2`
`=x^4-z^4+2x^3z-2xz^3-4x^2y^2+4y^2z^2`
`=(x^2-z^2)(x^2+z^2)+2xz(x^2-z^2)-4y^2(x^2-z^2)`
`=(x^2-z^2)(x^2+z^2+2xz-4y^2)`
`=(x^2-z^2)[(x+z)^2-(2y)^2]`
`=(x-z)(x+z)(x+z-2y)(x+z+2y)`
Thay `y=(x+z)/2` ta được :
`=(x-z)(x+z)(x+z-2*(x+z)/2)(x+z+2*(x+z)/2)`
`=(x-z)(x+z)[x+z-(x+z)](x+z+x+z)`
`=(x-z)(x+z)(x+z-x-z)(2x+2z)`
`=(x-z)(x+z)*0(2x+2z)=0`
Vậy `A = 0`.
