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)