Answer
$$(13-x)\cdot(16-x)\cdot(15-x)=-x^3+44x^2-643x+3120$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(13-x)\cdot(16-x)\cdot(15-x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(208-13x-16x+x^2)\cdot(15-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-29x+208)\cdot(15-x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15x^2-x^3-435x+29x^2+3120-208x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-x^3+44x^2-643x+3120\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{13-x}\right) $ by each term in $ \left( 16-x\right) $. $$ \left( \color{blue}{13-x}\right) \cdot \left( 16-x\right) = 208-13x-16x+x^2 $$ |
| ② | Combine like terms: $$ 208 \color{blue}{-13x} \color{blue}{-16x} +x^2 = x^2 \color{blue}{-29x} +208 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-29x+208}\right) $ by each term in $ \left( 15-x\right) $. $$ \left( \color{blue}{x^2-29x+208}\right) \cdot \left( 15-x\right) = 15x^2-x^3-435x+29x^2+3120-208x $$ |
| ④ | Combine like terms: $$ \color{blue}{15x^2} -x^3 \color{red}{-435x} + \color{blue}{29x^2} +3120 \color{red}{-208x} = -x^3+ \color{blue}{44x^2} \color{red}{-643x} +3120 $$ |
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