Answer
$$(x-3)(x-9)(x-4)=x^3-16x^2+75x-108$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-3)(x-9)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-9x-3x+27)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-12x+27)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2-12x^2+48x+27x-108 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-16x^2+75x-108\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-3}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x-3}\right) \cdot \left( x-9\right) = x^2-9x-3x+27 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-9x} \color{blue}{-3x} +27 = x^2 \color{blue}{-12x} +27 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-12x+27}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2-12x+27}\right) \cdot \left( x-4\right) = x^3-4x^2-12x^2+48x+27x-108 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} \color{blue}{-12x^2} + \color{red}{48x} + \color{red}{27x} -108 = x^3 \color{blue}{-16x^2} + \color{red}{75x} -108 $$ |
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