Question
Answer
$$(x^2-24x+24)(x-3)=x^3-27x^2+96x-72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-24x+24)(x-3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3-3x^2-24x^2+72x+24x-72 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-27x^2+96x-72\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-24x+24}\right) $ by each term in $ \left( x-3\right) $. $$ \left( \color{blue}{x^2-24x+24}\right) \cdot \left( x-3\right) = x^3-3x^2-24x^2+72x+24x-72 $$ |
| ② | Combine like terms: $$ x^3 \color{blue}{-3x^2} \color{blue}{-24x^2} + \color{red}{72x} + \color{red}{24x} -72 = x^3 \color{blue}{-27x^2} + \color{red}{96x} -72 $$ |
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