Answer
$$x(x-60)(x-230)x\cdot(-60)=-60x^4+17400x^3-828000x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x-60)(x-230)x\cdot(-60)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-60x)(x-230)x\cdot(-60) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3-230x^2-60x^2+13800x)x\cdot(-60) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-290x^2+13800x)x\cdot(-60) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(x^4-290x^3+13800x^2)\cdot(-60) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-60x^4+17400x^3-828000x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x-60\right) $ $$ \color{blue}{x} \cdot \left( x-60\right) = x^2-60x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-60x}\right) $ by each term in $ \left( x-230\right) $. $$ \left( \color{blue}{x^2-60x}\right) \cdot \left( x-230\right) = x^3-230x^2-60x^2+13800x $$ |
| ③ | Combine like terms: $$ x^3 \color{blue}{-230x^2} \color{blue}{-60x^2} +13800x = x^3 \color{blue}{-290x^2} +13800x $$ |
| ④ | $$ \left( \color{blue}{x^3-290x^2+13800x}\right) \cdot x = x^4-290x^3+13800x^2 $$ |
| ⑤ | $$ \left( \color{blue}{x^4-290x^3+13800x^2}\right) \cdot -60 = -60x^4+17400x^3-828000x^2 $$ |
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