Answer
$$(x-6)((x-9)^2-5)=x^3-24x^2+184x-456$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)((x-9)^2-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-6)(x^2-18x+81-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x-6)(x^2-18x+76) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-18x^2+76x-6x^2+108x-456 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-24x^2+184x-456\end{aligned} $$ | |
| ① | Find $ \left(x-9\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 9 }$. $$ \begin{aligned}\left(x-9\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 9 + \color{red}{9^2} = x^2-18x+81\end{aligned} $$ |
| ② | Combine like terms: $$ x^2-18x+ \color{blue}{81} \color{blue}{-5} = x^2-18x+ \color{blue}{76} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x-6}\right) $ by each term in $ \left( x^2-18x+76\right) $. $$ \left( \color{blue}{x-6}\right) \cdot \left( x^2-18x+76\right) = x^3-18x^2+76x-6x^2+108x-456 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-18x^2} + \color{red}{76x} \color{blue}{-6x^2} + \color{red}{108x} -456 = x^3 \color{blue}{-24x^2} + \color{red}{184x} -456 $$ |
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