Answer
$$(x^2-4x+2)(x-5)=x^3-9x^2+22x-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-4x+2)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^3-5x^2-4x^2+20x+2x-10 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-9x^2+22x-10\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-4x+2}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2-4x+2}\right) \cdot \left( x-5\right) = x^3-5x^2-4x^2+20x+2x-10 $$ |
| ② | Combine like terms: $$ x^3 \color{blue}{-5x^2} \color{blue}{-4x^2} + \color{red}{20x} + \color{red}{2x} -10 = x^3 \color{blue}{-9x^2} + \color{red}{22x} -10 $$ |
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