Answer
$$(x+6)(x+3)(x-5)=x^3+4x^2-27x-90$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+6)(x+3)(x-5)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x+6x+18)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+9x+18)(x-5) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-5x^2+9x^2-45x+18x-90 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+4x^2-27x-90\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+6}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x+6}\right) \cdot \left( x+3\right) = x^2+3x+6x+18 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} + \color{blue}{6x} +18 = x^2+ \color{blue}{9x} +18 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+9x+18}\right) $ by each term in $ \left( x-5\right) $. $$ \left( \color{blue}{x^2+9x+18}\right) \cdot \left( x-5\right) = x^3-5x^2+9x^2-45x+18x-90 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-5x^2} + \color{blue}{9x^2} \color{red}{-45x} + \color{red}{18x} -90 = x^3+ \color{blue}{4x^2} \color{red}{-27x} -90 $$ |
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