(x+1)^4+(x^2-1)^2+(x-1)^4因式分解

显示全部楼层 · 2007-7-12 21:46:35

(x+1)^4+(x^2-1)^2+(x-1)^4=[(x+1)^2]^2+2(x^2-1)^2+[(x-1)^2]^2-(x^2-1)^2=[(x+1)^2+(x-1)^2]^2-(x^2-1)^2=(2x^2+2)^2-(x^2-1)^2=(2x^2+2+x^2-1)(2x^2+2-x^2+1)=(3x^2+1)(x^2+3)

千问 · 2007-7-12 21:46:35

(x+1)^4+(x^2-1)^2+(x-1)^4=[(x+1)^2+(x-1)^2]^2-(x^2-1)^2=(3x^2+1)*(x^2+3)