因式分解1.x^6-y^6-2x^3+12.x^4+643.(x-3)(x-1)(x+2)(x+4)+244.(6x-1)(2x-1)(3x-1)(x-1)+x^2

Question

因式分解 1.x^6-y^6-2x^3+1 2.x^4+64 3.(x-3)(x-1)(x+2)(x+4)+24 4.(6x-1)(2x-1)(3x-1)(x-1)+x^2

Answer 1

1、
原式=(x^6-2x³+1)-y^6
=(x³-1)²-(y³)²
=(x²+y²-1)(x³-y³-1)
2.X^4+64=x^4+2^6=x^4+4×(2^4)=[x^4+4x²×2²+4×(2^4)]-4x²×2²=(x²+2×2²)²-(2x×2)²=(x²+8)²-(4x)²=
(x²+8-4x)(x²+8+4x)
3.(x-1)(x+2)(x-3)(x+4)+24
=(x²+x-2)(x²+x-12)+24
=(x²+x)²-12(x²+x)-2(x²+x)+24+24
=(x²+x)²-14(x²+x)+48
=(x²+x-6)(x²+x-8)
=(x+3)(x-2)(x²+x-8)
4.(6x-1)(2x-1)(3x-1)(x-1)+x^2
=[(6x-1)(x-1)][(2x-1)(3x-1)]+x^2
=[(6x^2+1)-7x][(6x^2+1)-5x]+x^2
=(6x^2+1)^2-12x(6x^2+1)+35x^2+x^2
=(6x^2+1)^2-12x(6x^2+1)+36x^2
=(6x^2+1)^2-2*(6x)*(6x^2+1)+(6x)^2
=(6x^2-6x+1)^2