X4次方-4X3次方＋4X²-1因式分解

X4次方-4X3次方＋4X²-1因式分解
X4次方-4X3次方＋4X²-1因式分解

X4次方-4X3次方＋4X²-1因式分解
x^4-4x^3+4x^2-1
=x^4-x^3-3x^3+3x^2+x^2-1
=x^3(x-1)-3x^2(x-1)+(x+1)(x-1)
=(x-1)(x³-3x²+x+1)
=(x-1)(x³-x²-2x²+2x-x+1)
=(x-1)[x²(x-1)-2x(x-1)-(x-1)]
=(x-1)²(x²-2x-1)