Question
Answer
$$(x-1)(x^2-5)(x-4)=x^4-5x^3-x^2+25x-20$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(x^2-5)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^3-5x-x^2+5)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4-5x^3-x^2+25x-20\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x^2-5\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x^2-5\right) = x^3-5x-x^2+5 $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^3-5x-x^2+5}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^3-5x-x^2+5}\right) \cdot \left( x-4\right) = x^4-4x^3-5x^2+20x-x^3+4x^2+5x-20 $$ |
| ③ | Combine like terms: $$ x^4 \color{blue}{-4x^3} \color{red}{-5x^2} + \color{green}{20x} \color{blue}{-x^3} + \color{red}{4x^2} + \color{green}{5x} -20 = x^4 \color{blue}{-5x^3} \color{red}{-x^2} + \color{green}{25x} -20 $$ |
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