Answer
$$(t-2)(t+5)(t-4)=t^3-t^2-22t+40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(t-2)(t+5)(t-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(1t^2+5t-2t-10)(t-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(1t^2+3t-10)(t-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}t^3-4t^2+3t^2-12t-10t+40 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}t^3-t^2-22t+40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{t-2}\right) $ by each term in $ \left( t+5\right) $. $$ \left( \color{blue}{t-2}\right) \cdot \left( t+5\right) = t^2+5t-2t-10 $$ |
| ② | Combine like terms: $$ t^2+ \color{blue}{5t} \color{blue}{-2t} -10 = t^2+ \color{blue}{3t} -10 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{t^2+3t-10}\right) $ by each term in $ \left( t-4\right) $. $$ \left( \color{blue}{t^2+3t-10}\right) \cdot \left( t-4\right) = t^3-4t^2+3t^2-12t-10t+40 $$ |
| ④ | Combine like terms: $$ t^3 \color{blue}{-4t^2} + \color{blue}{3t^2} \color{red}{-12t} \color{red}{-10t} +40 = t^3 \color{blue}{-t^2} \color{red}{-22t} +40 $$ |
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