`a)\sqrt{1-4a+4a^2}-2a`
`=\sqrt{1-2·1·2a+(2a)^2}-2a`
`=\sqrt{(1-2a)^2}-2a`
`=|1-2a|-2a`
+ Với `1-2a≥0<=>-2a≥-1<=>a≤1/2`
`|1-2a|-2a=1-2a-2a`
`=1-4a`
+ Với `1-2a<0<=>-2a<-1<=>a>1/2`
`|1-2a|-2a=-1+2a-2a`
`=-1`
`b)x-2y-\sqrt{x^2-4xy+4y^2}`
`=x-2y-\sqrt{x^2-2·x·2y+(2y)^2}`
`=x-2y-\sqrt{(x-2y)^2}`
`=x-2y-|x-2y|`
+ Với `x-2y≥0<=>x≥2y`
`x-2y-|x-2y|=x-2y-x+2y`
`=0`
+ Với `x-2y<0<=>x<2y`
`x-2y-|x-2y|=x-2y-2y+x`
`=2x-4y`
`c)x^2+\sqrt{x^4-8x^2+16}`
`=x^2+\sqrt{(x^2)^2-2·x^2·4+4^2}`
`=x^2+\sqrt{(x^2-4)^2}`
`=x^2+|x^2-4|`
+ Với `x^2-4≥0<=>`\(\left[ \begin{array}{l}x\geq2\\x\leq-2\end{array} \right.\)
`x^2+|x^2-4|=x^2+x^2-4=2x^2-4`
+ Với `x^2-4<0<=>-2<x<2`
`x^2+|x^2-4|=x^2+4-x^2=4`
