X+Y+Z-2XY-2YZ-2XZ注:第一行為冪的次數

熱心網友

注意觀察對稱性(y+x-z)*(y+x+z)*(-y+x+z)*(-y+x-z)

熱心網友

x^4+y^4+z^4-2*x^2*y^2-2*y^2*z^2-2*x^2*z^2= x^4+y^4+2*x^2*y^2-2*y^2*z^2-2*x^2*z^2+z^4-4*x^2*y^2= (x^2+y^2)^2-2*(x^2+y^2)*z^2+z^4-4*x^2*y^2= (x^2+y^2-z^2)^2-4*x^2*y^2= (x^2+y^2-z^2+2*x*y)*(x^2+y^2-z^2-2*x2*y)= [(x+y)^2-z^2]*[(x-y)^2-z^2]= (x+y+z)*(x+y-z)*(x-y+z)*(x-y-z)

熱心網友

x^4+y^4+z^4-2*x^2*y^2-2*y^2*z^2-2*x^2*z^2= x^4+y^4+2*x^2*y^2-2*y^2*z^2-2*x^2*z^2+z^4-4*x^2*y^2= (x^2+y^2)^2-2*(x^2+y^2)*z^2+z^4-4*x^2*y^2= (x^2+y^2-z^2)^2-4*x^2*y^2= (x^2+y^2-z^2+2*x*y)*(x^2+y^2-z^2-2*x2*y)= [(x+y)^2-z^2]*[(x-y)^2-z^2]= (x+y+z)*(x+y-z)*(x-y+z)*(x-y-z)