(x³+2x²+2x+1)因式分解

(x³+2x²+2x+1)

=(x^3+1)+2x(x+1)

=(x+1)(x^2-x+1)+2x(x+1)

=(x+1)[(x^2-x+1)+2x]

=(x+1)(x^2+x+1)

2011-11-23 20:58:14 補充：
a^3+b^3=(a+b)(a^2-ab+b^2)

x³+2x²+2x+1 = (x³+2x²+x)+(x+1) = x(x+1)² + (x+1) = (x+1){x(x+1)+1}
= (x+1)(x²+x+1}

x³+2x²+2x+1=(x³+x²+x)+(x²+x+1)=x(x²+x+1)+(x²+x+1)=(x²+x+1)(x+1)