Answer
$$x(x+3)(x^2+2x+2)=x^4+5x^3+8x^2+6x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x+3)(x^2+2x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x)(x^2+2x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4+2x^3+2x^2+3x^3+6x^2+6x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4+5x^3+8x^2+6x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x+3\right) $ $$ \color{blue}{x} \cdot \left( x+3\right) = x^2+3x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+3x}\right) $ by each term in $ \left( x^2+2x+2\right) $. $$ \left( \color{blue}{x^2+3x}\right) \cdot \left( x^2+2x+2\right) = x^4+2x^3+2x^2+3x^3+6x^2+6x $$ |
| ③ | Combine like terms: $$ x^4+ \color{blue}{2x^3} + \color{red}{2x^2} + \color{blue}{3x^3} + \color{red}{6x^2} +6x = x^4+ \color{blue}{5x^3} + \color{red}{8x^2} +6x $$ |
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