1、 x²-y²+x³-y³
=(x²-y²)+(x³-y³)
=(x+y)(x-y)+(x-y)(x^2+xy+y^2)
=(x-y)(x+y+x^2+xy+y^2)
=(x-y)(x^2+y^2+xy+x+y)
2、 (a+1)(a+3)(a+5)(a+7)+15
=[(a+)(a+7)][(a+3)(a+5)]+15
=(a^2+8a+7)(a^2+8a+15)+15
=(a^2+8a)^2+22(a^2+8a)+105+15
=(a^2+8a)^2+22(a^2+8a)+120
=(a^2+8a+10)(a^2+8a+12)
=(a^2+8a+10)(a+2)(a+6)
3、 a(a-b+2)-6b(b+1)
=a^2-ab+2a-6b^2-6b
=(a^2-ab-6b^2)+(2a-6b)
=(a-3b)(a+2b)+2(a-3b)
=(a-3b)(a+2b+2)