>誰かx^3-6x^2+9x-4の因数分解お願いします
(a-b)^3=(a-b)(a^2+ab+b^2)…(☆)

x^3-6x^2+9x-4
=x(x^2-6x+9)-4
=x(x-3)^2-4
=x(x-3)^2-4x^3+4x^3-4
=x{(x-3)+2x}{(x-3)-2x}+4(x^3-1)
=-3x(x-1)(x+3)+4(x-1)(x^2+x+1) ∵(☆)
=(x-1){-3x(x+3)+4(x^2+x+1)}
=(x-1)(x^2-5x+4)=(x-1)^2(x-4)