Answer
$$(x-2)(x+3)(x+4)=x^3+5x^2-2x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x+3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-2x-6)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+x-6)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+4x^2+x^2+4x-6x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+5x^2-2x-24\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x+3\right) = x^2+3x-2x-6 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{3x} \color{blue}{-2x} -6 = x^2+ \color{blue}{x} -6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+x-6}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^2+x-6}\right) \cdot \left( x+4\right) = x^3+4x^2+x^2+4x-6x-24 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{4x^2} + \color{blue}{x^2} + \color{red}{4x} \color{red}{-6x} -24 = x^3+ \color{blue}{5x^2} \color{red}{-2x} -24 $$ |
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