1.

1) m^3+125n^3=(m+5n)(m^2-5mn+25)

2) xy^2-16x^3=x(y^2-16x^2)=x(y-4x)(y+4x)

3) -5x^2+30x-45=-5(x^2-6x+9)=-5(x-3)^2

4) 7xy-42x+14y-84=7(xy-6x+2y-12)=

=7(-6(x+2)+y(x+2))=7(x+2)(y-6)

5) 10000-c^4=(100-c^2)(100+c^2)

2.

b(b-3)(b+3)-(b-1)(b^2+b+1)=b(b^2-9)-(b^3-1)=b^3-9b-b^3+1=1-9b

3.

1) 81с^2-d^2+9c+d=(9c-d)(9c+d)+(9c+d)=(9c+d)(9c-d+1)

2) a^2+8ab+16b^2-1=(a+4b)^2-1=(a+4b-1)(a+4b+1)

3) ax^6-3x^6-ax^3+3x^3=x^3(ax^3-3x^3-a+3)=-3(x^3-1)+a(x^3-1)=(x^3-1)(a-3)

4) 25-m^2-12mn-36n^2=25-(m^2+12mn+36n^2)=25-(m+6n)^2=(5-m-6n)(5+m+6n)