Answer
$$(x-2)(x-4)(x-5)=x^3-11x^2+38x-40$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x-4)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-4x-2x+8)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-6x+8)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-5x^2-6x^2+30x+8x-40 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-11x^2+38x-40\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x-4\right) = x^2-4x-2x+8 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-4x} \color{blue}{-2x} +8 = x^2 \color{blue}{-6x} +8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-6x+8}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2-6x+8}\right) \cdot \left( x-5\right) = x^3-5x^2-6x^2+30x+8x-40 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-5x^2} \color{blue}{-6x^2} + \color{red}{30x} + \color{red}{8x} -40 = x^3 \color{blue}{-11x^2} + \color{red}{38x} -40 $$ |
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