Originally Posted by

**jimmic** Now, the very next paragraph I was presented with this (x - 1)^2 - 4 = 0 and the simple solution that x = 3 or -1. Then my problem begins as the author goes on to say that the equation (x - 1)^2 - 4 can be "simplified" to x^2 - 2x - 3. How is this possible?

We can use the difference of perfect squares as follows

$\displaystyle

\begin{aligned}

\left( {x - 1} \right)^2 - 4 &= 0\\

\left[ {\left( {x - 1} \right) + 2} \right]\left[ {\left( {x - 1} \right) - 2} \right] &= 0\\

\left( {x + 1} \right)\left( {x - 3} \right) &= 0\\

x^2 - 2x - 3 &= 0

\end{aligned}

$

$\displaystyle \emph{As desired}~\blacksquare$

P.S.: actually, the last step isn't necessary to get the roots of the equation.