Answer
$$(x+2)(x-5)(x+9)=x^3+6x^2-37x-90$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x-5)(x+9)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-5x+2x-10)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-3x-10)(x+9) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+9x^2-3x^2-27x-10x-90 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+6x^2-37x-90\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x-5\right) = x^2-5x+2x-10 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-5x} + \color{blue}{2x} -10 = x^2 \color{blue}{-3x} -10 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-3x-10}\right) $ by each term in $ \left( x+9\right) $. $$ \left( \color{blue}{x^2-3x-10}\right) \cdot \left( x+9\right) = x^3+9x^2-3x^2-27x-10x-90 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{9x^2} \color{blue}{-3x^2} \color{red}{-27x} \color{red}{-10x} -90 = x^3+ \color{blue}{6x^2} \color{red}{-37x} -90 $$ |
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