To simplify the expression A=√(1-4a+4a^) - 2a, we can start by expanding the square term:

A=√(1-4a+4a^2) - 2a

Next, we can simplify the square root term by factoring the quadratic expression inside:

A=√((1-2a)^2) - 2a

Since the square root of a square is the absolute value of the expression inside, we can remove the square root:

A=|1-2a| - 2a

Finally, we can simplify further by distributing the negative sign:

A=2a-1 - 2a

The "2a" terms cancel out, leaving us with:

A=-1