`= 1^2 - (2a)^2 - a^2 - 2a`.
`= 1 - 5a^2 - 2a`.
\(\left(1+2a\right)\left(1-2a\right)-a\left(a+2\right)\)
\(=1-4a^2-a^2-2a\)
\(=-5a^2-2a+1\)
\(=-5\left(a^2+\dfrac{2}{5}a\right)+1\)
\(=-5\left(a^2+\dfrac{2}{5}a+\dfrac{1}{25}-\dfrac{1}{25}\right)+1\)
\(=-5\left(a+\dfrac{1}{5}\right)^2+1+\dfrac{1}{5}\)
\(=\dfrac{6}{5}-5\left(a+\dfrac{1}{5}\right)^2\)
\(=\dfrac{1}{5}\left[6-25\left(a+\dfrac{1}{5}\right)^2\right]\)
\(=\dfrac{1}{5}\left[\sqrt{6}+5\left(a+\dfrac{1}{5}\right)\right]\left[\sqrt{6}-5\left(a+\dfrac{1}{5}\right)\right]\)
\(=\dfrac{1}{5}\left(5a+1+\sqrt{6}\right)\left(5a-1+\sqrt{6}\right)\)
