因式分解(1-2x)^2(1+2x+4x^2)-(1+8x^3)^2
问题描述：
因式分解(1-2x)^2(1+2x+4x^2)-(1+8x^3)^2
答
(1-2x)^2(1+2x+4x^2)-(1+8x^3)^2
=(1-8x^3)^2 -(1+8x^3)^2
=(1-8x^3+1+8x^3)(1-8x^3-1+8x^3)
=-32x^3
答
(1-2x)^2(1+2x+4x^2)-(1+8x^3)^2
=(2x-1)^2(1+2x+4x^2)-(8x^3+1)^2
=(8x^3-1)^2-(8x^3+1)^2
=[(8x^3-1)-(8x^3+1)][(8x^3-1)+(8x^3+1)]
=(8x^3-1-8x^3-1)(8x^3-1+8x^3+1)
=(-2)*16x^3
=-32x^3
答
=(1-2x)(1-8x^3)-(1+8x^3)^2=16x^4-8x^3-2x+1-(64x^6+16x^3+1)=-64x^6+16x^4-24x^3-2x=-2x(32x^5-8x^3+12x^2+1)