Answer
$$(n+k-2)(n+k-1)=k^2+2kn+n^2-3k-3n+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(n+k-2)(n+k-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}k^2+2kn+n^2-3k-3n+2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{n+k-2}\right) $ by each term in $ \left( n+k-1\right) $. $$ \left( \color{blue}{n+k-2}\right) \cdot \left( n+k-1\right) = n^2+kn-n+kn+k^2-k-2n-2k+2 $$ |
| ② | Combine like terms: $$ n^2+ \color{blue}{kn} \color{red}{-n} + \color{blue}{kn} +k^2 \color{green}{-k} \color{red}{-2n} \color{green}{-2k} +2 = k^2+ \color{blue}{2kn} +n^2 \color{green}{-3k} \color{red}{-3n} +2 $$ |
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