Answer
$$(x-5)(x-6)(x-9)=x^3-20x^2+129x-270$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-5)(x-6)(x-9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-6x-5x+30)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-11x+30)(x-9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-9x^2-11x^2+99x+30x-270 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-20x^2+129x-270\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-5}\right) $ by each term in $ \left( x-6\right) $. $$ \left( \color{blue}{x-5}\right) \cdot \left( x-6\right) = x^2-6x-5x+30 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-6x} \color{blue}{-5x} +30 = x^2 \color{blue}{-11x} +30 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-11x+30}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x^2-11x+30}\right) \cdot \left( x-9\right) = x^3-9x^2-11x^2+99x+30x-270 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-9x^2} \color{blue}{-11x^2} + \color{red}{99x} + \color{red}{30x} -270 = x^3 \color{blue}{-20x^2} + \color{red}{129x} -270 $$ |
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