Question
Answer
$$(x^2-5x-24)(x-8)=x^3-13x^2+16x+192$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-5x-24)(x-8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3-8x^2-5x^2+40x-24x+192 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-13x^2+16x+192\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-5x-24}\right) $ by each term in $ \left( x-8\right) $. $$ \left( \color{blue}{x^2-5x-24}\right) \cdot \left( x-8\right) = x^3-8x^2-5x^2+40x-24x+192 $$ |
| ② | Combine like terms: $$ x^3 \color{blue}{-8x^2} \color{blue}{-5x^2} + \color{red}{40x} \color{red}{-24x} +192 = x^3 \color{blue}{-13x^2} + \color{red}{16x} +192 $$ |
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