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