$(2x^2+4x+xy+2y)$
=$2x(x+2)+y(x+2)$
=$(x+2)(2x+y)$
$(x^2+xy-7x-7y)$
=$x(x+y)-7(x+y)$
=$(x+y)(x-7)$
$(ac+bc+a+b)$
=$c(a+b)+(a+b)$
=$(a+b)(c+1)$
$(7z^2-7yz-4z+4y)$
=$7z(z-y)-4(z-y)$
=$(z-y)(7z-4)$
$(x^3+3x^2+3x+9)$
=$x^2(x+3)+3(x+3)$
=$(x+3)(x^2+3)$
$(pq-p^2-5(p-q))$
=$p(q-p)+5(q-p)$
=$(q-p)(p+5)$
$(y^2+1+2y-49)$
=$(y^2+2y+1)-49$
=$(y+1)^2-7^2$
=$(y+1-7)(y+1+7)$
=$(y-6)(y+8)$
$(36a^2-c^2-9b^2-6bc)$
=$[(6a)^2-(c^2+6bc+9b^2)$
=$[(6a)^2-(c+3b)^2]$
=$(6a-3b-c)(6a+3b+c)$
$(ab(a-b)+b^2c-bc^2+c^2a-ca^2($
=$a^2b-ab^2+b^2c-bc^2+c^2a-ca^2$
=$(a^2b-bc^2)+(-ab^2+b^2c)+(c^2a-ca^2)$
=$b(a^2-c^2)-b^2(a-c)-ca(a-c)$
=$b(a-c)(a+c)-b^2(a-c)-ca(a-c)$
=$(a-c)(ab+bc-b^2-ca)$
=$(a-c)[(ab-b^2)+(bc-ca)]$
=$(a-c)[b(a-b)-c(a-b)]$
=$(a-b)(b-c)(a-c)$
