Answer
$$(x-5)(x-9)(x-11)=x^3-25x^2+199x-495$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-5)(x-9)(x-11)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-9x-5x+45)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-14x+45)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-11x^2-14x^2+154x+45x-495 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-25x^2+199x-495\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-5}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x-5}\right) \cdot \left( x-9\right) = x^2-9x-5x+45 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-9x} \color{blue}{-5x} +45 = x^2 \color{blue}{-14x} +45 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-14x+45}\right) $ by each term in $ \left( x-11\right) $. $$ \left( \color{blue}{x^2-14x+45}\right) \cdot \left( x-11\right) = x^3-11x^2-14x^2+154x+45x-495 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-11x^2} \color{blue}{-14x^2} + \color{red}{154x} + \color{red}{45x} -495 = x^3 \color{blue}{-25x^2} + \color{red}{199x} -495 $$ |
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