`a, (x-1)^2 - 4 = 0`
`<=> (x-3)(x+1) = 0`
`=> x - 3 = 0`
`x + 1 = 0`
`=> x = 3`
`x = -1`
b, `x^2 - x = - 2 + 2`
`<=> x^2 - x = 0`
`<=> x(x-1) = 0`
`=> x = 0`
`x - 1 = 0`
`=> x = 0`
`x = 1`.
\(a,\left(x-1\right)^2-2^2=0\\
\Leftrightarrow\left(x-1-2\right)\left(x-1+2\right)=0\\
\Leftrightarrow\left(x-3\right)\left(x+1\right)=0\\
\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\\
\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
\(b,x^2-x=0\\
\Leftrightarrow x\left(x-1\right)=0\\
\Leftrightarrow\left[{}\begin{matrix}x-1=0\Leftrightarrow x=1\\x=0\end{matrix}\right.\)