1.a^2+8ab+7b^2+a+b
=(a+b)(a+7b)+(a+b)
=(a+b)(a+7b+1)
2.（x^2+2x)-7(x^2+2x)-8
=[(x^2+2x)-8][(x^2+2x)+1]
=(x+4)(x-2)(x+1)^2
3.x^2+xy-6y^2+x+13y-6
=(x+3y)(x-2y)+x+13y-6
=(x+3y)(x-2y)+(3x+9y)-2x+2y-6
=(x+3y)(x-2y)+3(x+3y)-2(x-2y+3)
=((x+3y)(x-2y+3)-2(x-2y+3)
=(x-2y+3)(x+3y-2)
4.(x+3)(x-5)(x+6)(x-10)-20x^2
=[(x+3)(x-10)][(x-5)(x+6)]-20x^2
=[(x^2-30)-7x][(x^2-30)+x]-20x^2
=(x^2-30)^2-6x(x^2-30)-7x^2-20x^2
=(x^2-30)^2-6x(x^2-30)-27x^2
=(x^2-9x-30)(x^2+3x-30)
5.x^3-2x^2(y-2)+x(y-2)^2
=x[x^2-2x(y-2)+(y-2)^2]
=x[x-(y-2)]^2
=x(x-y+2)^2