(x+3)(x+4)(x+5)(x+6)=[(x+3)(x+6)][(x+4)(x+5)]=(x^2+9x+18)(x^2+9x+20)=(x^2+9x)^2+38(x^2+9x)+360=x^4+18x^3+81x^2+38x^2+342x+360=x^4+18x^3+119x^2+342x+360.