Question
Answer
$$(x+1)(x-2)(x+6)=x^3+5x^2-8x-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+1)(x-2)(x+6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-2x+x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-x-2)(x+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+6x^2-x^2-6x-2x-12 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+5x^2-8x-12\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+1}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x+1}\right) \cdot \left( x-2\right) = x^2-2x+x-2 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-2x} + \color{blue}{x} -2 = x^2 \color{blue}{-x} -2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-x-2}\right) $ by each term in $ \left( x+6\right) $. $$ \left( \color{blue}{x^2-x-2}\right) \cdot \left( x+6\right) = x^3+6x^2-x^2-6x-2x-12 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{6x^2} \color{blue}{-x^2} \color{red}{-6x} \color{red}{-2x} -12 = x^3+ \color{blue}{5x^2} \color{red}{-8x} -12 $$ |
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