algebra help in AoCP intro to induction In the introduction of mathematical induction, section 1.2.1 of Knuth's Art of Computer Programming, I'm struggling with (4) especially this relation:
$\phi^{n-2} +\phi^{n-1} = \phi^{n-2}(1+\phi)$
Looks like my algebra skills have gone all to rot, if I ever had any, so I am hoping someone can provide a detailed expansion of how these two forms are equal. 

Distributing and using properties of exponents,
\begin{align*}
\phi^{n - 2} (1 + \phi) &= \phi^{n - 2} \cdot 1 + \phi^{n - 2} \cdot \phi^1 \\
&= \phi^{n - 2} + \phi^{n - 1}
\end{align*}
