4x3+8x2-x-2 =4x^2(x+2)-(x+2)=(4x^2-1)(x+2)=(2x+1)(2x-1)(x+2)
x3+x2y-xy2-y3 =x^2(x+y)-y^2(x+y)=(x+y)^2(x-y)
x2y-xy2+2x-2y=xy(x-y)+2(x-y)=(x-y)(xy+2)
x2-4y2-x+2y=(x+2y)(x-2y)-(x-2y)=(x+2y-1)(x-2y)
ac-bc-a2+2ab-b2=c(a-b)-(a-b)^2=(c-a+b)(a-b)
a3+a2b-a2c-abc=a^2(a+b)-ac(a+b)=a(a-c)(a+b)
7)x2-2x-b2-2b=(x+b)(x-b)-2(x+b)=(x+b)(x-b-2)
8)5a2m+6abm-10a2n-12abn=am(5a+6b)-2an(5a+6b)=a(m-2n)(5a+6b)
9)-xy+bx+ay-ab=x(b-y)-a(b-y)=(x-a)(b-y)
10)a(b-c)+a2-bc=a(b+a)-c(a+b)=(a-c)(a+b)
11)x2-y2+2y-1=x^2-(y-1)^2=(x+y-1)(x-y+1)
12)a2-b2-c2+2bc=a^2-(b-c)^2=(a+b-c)(a-b+c)
13)x2+4y-1-4y2=x^2-(2y-1)^2=(x+2y-1)(x-2y+1)
14)4-a2+4ab-4b2=2^2-(a-b)^2=(2+a-b)(2-a+b)
15)x2+8xy+16y2+3x+12y+2=(x+4y)^2+3(x+4y)+2=(x+4y+1)(x+4y+2)
16)a2-3a+b2-3b+2ab-54=(a+b)^2-3(a+b)-54=(a+b-9)(a+b+6)