1因式分解(x+1)(x-6)-8 因式分解(2y^2+5y+1)(2y^2+5y-6) 2因式分解 6x^2+xy-2y^2 2x^2-xy+2x-y 因式分解 10x^2-xy-2y^2+4x-2y 3因式分解a^6-b^6 因式分解 (x+y)^6-(x-y)^6?

1a)因式分解(x+1)(x－6)－8
Sol
(x+1)(x－6)－8
=x^2－5x－6－8
=x^2－5x－14
=(x－7)(x+2)
1b)由此因式分解(2y^2+5y+1)(2y^2+5y－6)－8
Sol
(2y^2+5y+1)(2y^2+5y－6)－8
=[(2y^2+5y)+1]*[(2y^2+5y)－6]－8
=(2y^2+5y－7)(2y^2+5y+2)
=(2y+7)(y－1)(2y+1)(y+2)
2a)因式分解 6x^2+xy－2y^2 2x^2－xy+2x－y
Sol
6x^2+xy－2y^2
=(3x+2y)(2x－y)
2x^2－xy+2x－y
=(2x^2+2x)－(xy+y)
=2x(x+1)－y(x+1)
=(2x－y)(x+1)
2b)由此因式分解 10x^2－xy－2y^2+4x－2y
Sol
10x^2－xy－2y^2+4x－2y
=(6x^2+xy－2y^2)+(4x^2－2xy+4x－2y)
=(6x^2+xy－2y^2)+2(2x^2－xy+2x－y)
=(3x+2y)(2x－y)+2(2x－y)(x+1)
=(3x+2y+2x+2)(2x－y)
=(5x+2y+2)(2x－y)
3a)因式分解a^6－b^6
Sol
a^6－b^6
=(a^3－b^3)(a^3+b^3)
=(a－b)(a^2+ab+b^2)(a+b)(a^2－ab+b^2)
3b)由此因式分解 (x+y)^6－(x－y)^6
Sol
(x+y)^6－(x－y)^6
=[(x+y)－(x－y)]*[(x+y)^2+(x+y)(x－y)+(x－y)^2]*[(x+y)+(x－y)]*[(x+y)^2
－(x+y)(x－y)+(x－y)^2)
=(2y)(x^2+2xy+y^2+x^2－y^2+x^2－2xy+y^2)(2x)(x^2+2xy+y^2
－x^2+y^2+x^2－2xy+y^2)
=(2y)(3x^2+y^2)(2x)(x^2+3y^2)
=4xy(x^2+3y^2)(3x^2+y^2)