Answer
$$(x+2)(x-3)(x+4)=x^3+3x^2-10x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x-3)(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-3x+2x-6)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-x-6)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+4x^2-x^2-4x-6x-24 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+3x^2-10x-24\end{aligned} $$ | |
| 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: $$ x^3+ \color{blue}{4x^2} \color{blue}{-x^2} \color{red}{-4x} \color{red}{-6x} -24 = x^3+ \color{blue}{3x^2} \color{red}{-10x} -24 $$ |
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