Answer
$$(x^2+9)(x^2+4)(x+2)=x^5+2x^4+13x^3+26x^2+36x+72$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+9)(x^2+4)(x+2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^4+4x^2+9x^2+36)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^4+13x^2+36)(x+2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^5+2x^4+13x^3+26x^2+36x+72\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+9}\right) $ by each term in $ \left( x^2+4\right) $. $$ \left( \color{blue}{x^2+9}\right) \cdot \left( x^2+4\right) = x^4+4x^2+9x^2+36 $$ |
| ② | Combine like terms: $$ x^4+ \color{blue}{4x^2} + \color{blue}{9x^2} +36 = x^4+ \color{blue}{13x^2} +36 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4+13x^2+36}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^4+13x^2+36}\right) \cdot \left( x+2\right) = x^5+2x^4+13x^3+26x^2+36x+72 $$ |
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