1.解:(1)ap-aq+am=a(p-q+m).
(2)4x²-8xy+2x=2x(2x-4y+1).
(3)12xyz-9x²y=3xy(4z-3x).
(5)6a²b-9ab²+15ab=3ab(2a-3b+5).
2.解:(1)4ab(2x-y)+b(2x-y)=b(2x-y)(4a+1);
(2)6a(1-b) ²-2(b-1) ²=2(b-1) ²•(3a-1).
3.解:(1)1-16a²=(1+4a)(1-4a);
(2)m²-9n²=(m+3n)(m-3n);
(3)4x²-81y²=(2x) ²-(9y²)=(2x+9y)(2x-9y);
(4)9a²x²-b²y²=(3ax+by)(3ax-by).
4.解:(1)(x+5) ²-4=(x+5) ²-2²=(x+5+2)(x+5-2)=(x+7)(x+3);
(2)(a+b) ²-a²=(a+b+a)(a+b-a)=b(2a+b);
(3)(a²+b²)²-a²b²=(a²b²+ab)(a²b²-ab);
(4)49(a-b)²-16(a+b)²
=[7(a-b)] ²-[4(a+b)] ²
=[7(a-b)+4(a+b)][7(a-b)-4(a-b)]
=(7a-7b+4a+4b)(7a-7b-4a-4b)
=(11a-3b)(3a-11b).
5.解:(1)a²b²-2ab+1=(ab-1)²;
(2)9-12a+4a²=(2a-3)²;
(3)4x²+4x+1=(2x+1)²;
(4)x²-6xy+9y²=(x-3y)².
6.解:(1)(a+b)²+6(a+b)+9=(a+b+3)²;
(2)16-24(x-y)+9(x-y)²=[3(x-y)-4]²=(3x-3y-4)²;
(3)a²-2a(b+c)+(b+c)²=[a-(b+c)]²=(a-b-c)²;
(4)4x²-4x(y-1)+(y-1)²=[2x-(y-1)]²=(2x-y+1) ².
7.解:(1)-a+2a²-a³=-a(1-2a-2²)=-a(a-1)²;
(2)3ax²-3ay²=3a(x²-y²)=2a(x+y)(x-y);
(3)16a²b-13a²-4ab²=-4a(4a²-4ab+b²)=-4a(2a-b) ²;
(4)x²(y²-1)+(1-y²)=(y²-1)(x²-1)=(y+1)(y-1)(x+1)(x-1).