因式分解 (X²+1)-4X(X²+1)+4X²

问题描述:

因式分解 (X²+1)-4X(X²+1)+4X²

(X²+1)²-4X(X²+1)+4X²
=(x²+1)²-2×(x²+1)×2x+(2x)²
=[(x²+1)-2x]²
=[(x-1)²]²
=(x-1)^4

(X²+1)-4X(X²+1)+4X²
=(X²+1-2X)²
=(X-1)⁴