Question
Answer
$$(r-1)(r^2-2r+3)=r^3-3r^2+5r-3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(r-1)(r^2-2r+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}r^3-2r^2+3r-r^2+2r-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}r^3-3r^2+5r-3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{r-1}\right) $ by each term in $ \left( r^2-2r+3\right) $. $$ \left( \color{blue}{r-1}\right) \cdot \left( r^2-2r+3\right) = r^3-2r^2+3r-r^2+2r-3 $$ |
| ② | Combine like terms: $$ r^3 \color{blue}{-2r^2} + \color{red}{3r} \color{blue}{-r^2} + \color{red}{2r} -3 = r^3 \color{blue}{-3r^2} + \color{red}{5r} -3 $$ |
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