Answer
$$(3+x)\cdot(5+x)\cdot(11+x)=x^3+19x^2+103x+165$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3+x)\cdot(5+x)\cdot(11+x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(15+3x+5x+x^2)\cdot(11+x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+8x+15)\cdot(11+x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}11x^2+x^3+88x+8x^2+165+15x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+19x^2+103x+165\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{3+x}\right) $ by each term in $ \left( 5+x\right) $. $$ \left( \color{blue}{3+x}\right) \cdot \left( 5+x\right) = 15+3x+5x+x^2 $$ |
| ② | Combine like terms: $$ 15+ \color{blue}{3x} + \color{blue}{5x} +x^2 = x^2+ \color{blue}{8x} +15 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+8x+15}\right) $ by each term in $ \left( 11+x\right) $. $$ \left( \color{blue}{x^2+8x+15}\right) \cdot \left( 11+x\right) = 11x^2+x^3+88x+8x^2+165+15x $$ |
| ④ | Combine like terms: $$ \color{blue}{11x^2} +x^3+ \color{red}{88x} + \color{blue}{8x^2} +165+ \color{red}{15x} = x^3+ \color{blue}{19x^2} + \color{red}{103x} +165 $$ |
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