x^2-3x-6y-4y^2 a^2-ab^2+a-b x^2-4y^2+4yz-z^2 4a^2-4b^2+4a+1 -25+a^2+9b^2-6ab

(1）x^2-3x-6y-4y^2
=(x+2y)(x-2y)-3(x+2y)
=(x+2y)(x-2y-3)

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

(3)a^2b-ab^2+a-b
=ab(a-b)+(a-b)
=(ab-1)(a-b)

(4)x^2-4y^2+4yz-z^2
=x^2-(4y^2-4yz+z^2)
=x^2-(2y-z)^2
=(x+2y-z)(x-2y+z)

(5)4a^2-4b^2+4a+1
=(4a^2+4a+1)-4b^2
=(2a+1)^2-4b^2
=(2a+2b+1)(2a-2b+1)

(6)-25+a^2+9b^2-6ab
=(a-3b)^2-25
=(a-3b+5)(a-3b-5)

a^2+4a+b^2-6b+13=0,
(a+2)^2+(b-3)^2=0,
a=-2,b=3,
a^2+2b
=4+6=10

121(x+y)^2-169(x-y)^2
=(11x+11y+13x-13y)(11x+11y-13x+13y)
=(24x-2y)(24y-2x)
=4(12x-y)(12y-x)

4a(a-3)^2+8a^2(3-a)
=4a(a-3)(a-3-2a)
=4a(a-3)(-a-3)
=-4a(a-3)(a+3)