(x^2-6x+1)(x^2+x+1)+12x^2因式分解

问题描述:

(x^2-6x+1)(x^2+x+1)+12x^2因式分解

最后结果是(x-1)^2+(x^2-3x+1)
方法就是先把式子全部展开,然后再分解
可以自己再做一下,结果不一定正确

(x^2-6x+1)(x^2+x+1)+12x^2=(x^2+1)^2-5x(x^2+1)-6x^2+12x^2=(x^2+1)^2-5x(x^2+1)+6x^2=(x^2+1-2x)(x^2+1-3x)=(x-1)^2)(x^2+1-3x)

(x^2-6x+1)(x^2+x+1)+12x^2=(x^2+1)^2-5x(x^2+1)-6x^2+12x^2
=(x^2+1)^2-5x(x^2+1)+6x^2=(x^2+1-2x)(x^2+1-3x)=(x-1)^2(x^2-3x+1)