1.∵|3x+y-2|+（2x+3y+1)^2=0,∴3x+y-2=0,2x+3y+1=0,解得：x=3,y=-7.
2.4x^3y+4x^2y^2+xy^3=(2xy+y^2)(2x^2+xy)
3.5a^2b(x-y)^3-30ab^2(y-x)^2=5a^2b(x-y)^3+30ab^2(x-y)^2=5ab(x-y)^2[a(x-y)+6b]
4.(a-b)^3-(a-b)=(a-b)[(a-b)^2-1]=(a-b)(a-b-1)(a-b+1)
5.(x^2-2)^2-14(x^2-2)+49=(x^2-2-7)^2=(x^2-9)^2=(x^2-3^2)^2=(x-3)^2(x+3)^2
6.(a^2+ab+b^2)^2-9a^2b^2=(a^2+ab+b^2)^2-(3ab)^2=(a^2+ab+b^2-3ab)(a^2+ab+b^2+3ab)=(a^2-2ab+b^2)(a^2+4ab+b^2)=(a-b)^2[(a-b)^2+6ab]