Question

\(\sqrt{1-4a+4a^2}-2a\)

 

 

Answer 1

\(\sqrt{1-4a+4a^2}-2a\left(1\right)=\sqrt{\left(1-2a\right)^2}-2a=\left|1-2a\right|-2a\)

TH1: \(a\le\dfrac{1}{2}\)

\(\left(1\right)=1-2a-2a=1-4a\)

TH2: \(a>\dfrac{1}{2}\)

\(\left(1\right)=2a-1-2a=-1\)

Answer 2

\(\sqrt{4a^2-4a+1}-2a\)

\(=\left|2a-1\right|-2a\)

\(=\left[{}\begin{matrix}2a-1-2a=-1\left(a\ge\dfrac{1}{2}\right)\\1-2a-2a=1-4a\left(a< \dfrac{1}{2}\right)\end{matrix}\right.\)