(1/2x+1/3y+1/4)(2x+3y+4)=x^2+3xy/2+2x+2xy/3+y^2+4y/3+x/2+3y/4+1=x^2+y^2+13xy/6+5x/2+25y/12+1;x^2-2x-4y^2-4y=(x^2-2x+1)-(4y^2+4y+1)=(x-1)^2-(2y+1)^2=[(x-1)+(2y+1)][(x-1)-(2y+1)]=(x+2y)(x-2y-2).