Lösung 2.1:3f

Treating \displaystyle 4x as one term, we can write

\displaystyle \qquad 16x^2+8x+1=(4x)^2 +2\cdot 4x +1

and since \displaystyle y^2 +2y+1=(y+1)^2 we obtain

\displaystyle \qquad (4x)^2 +2\cdot 4x +1= (4x+1)^2