Bài 3:

a, $18a^3b^2-9a^2b^3$

$=9a^2b^2.(2a-b)$

b, $x^2-6xy+9y^2-36$

$=(x-3y)^2-36$

$=(x-3y-6)(x-3y+6)$

c, $2x^2-2xy-x+y$

$=2x(x-y)-(x-y)$

$=(x-y)(2x-1)$

d, $x^2+6x-4y^2+9$

$=(x^2+6x+9)-4y^2$

$=(x+3)^2-4y^2$

$=(x+3-2y)(x+3+2y)$

Bài 4:

Ta có: $x-y=-5$

$⇒(x-y)^2=(-5)^2$

$⇒x^2-2xy+y^2=25$

$⇒x^2+y^2=25+2.(-6)$

$⇒x^2+y^2=13$

$x^3-y^2-x^2+2xy-y^2$

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

$=-5.(x^2+y^2-6)-(x-y)^2$

$=-5.(13-6)-(-5)^2$

$=-5.7-25$

$=-60$

Bài 3 :

a) $18a^3b^2-9a^2b^3$

$=9a^2b^2.(2a-b)$

b) $x^2-6xy+9y^2-36$

$=(x^2-6xy+9y^2)-6^2$

$=(x-3y)^2-6^2$

$(x-3y-6)(x-3y+6)$

c) $2x^2-2xy-x+y$

$=2x.(x-y) -(x-y)$

$=(x-y),(2x-1) $

d) $x^2+6x-4y^2+9$

$=(x^2+6x+9)-(2y)^2$

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

$=(x-2y+3).(x+2y+3)$

Bài 4 : 

Ta có : $x^3-y^3-x^2+2xy-y^2$

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

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

Thay $x-y=-5,x.y=-6$ vào biểu thức ta có :

$(-6)^3+3.(-5).(-6)-5^2$

$=-151$