Question
Answer
$$(x-6)(x-9)(x-11)=x^3-26x^2+219x-594$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)(x-9)(x-11)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-9x-6x+54)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-15x+54)(x-11) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-11x^2-15x^2+165x+54x-594 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-26x^2+219x-594\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-6}\right) $ by each term in $ \left( x-9\right) $. $$ \left( \color{blue}{x-6}\right) \cdot \left( x-9\right) = x^2-9x-6x+54 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-9x} \color{blue}{-6x} +54 = x^2 \color{blue}{-15x} +54 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-15x+54}\right) $ by each term in $ \left( x-11\right) $. $$ \left( \color{blue}{x^2-15x+54}\right) \cdot \left( x-11\right) = x^3-11x^2-15x^2+165x+54x-594 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-11x^2} \color{blue}{-15x^2} + \color{red}{165x} + \color{red}{54x} -594 = x^3 \color{blue}{-26x^2} + \color{red}{219x} -594 $$ |
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