Question
Answer
$$(x-6)(x+3)(x+1)=x^3-2x^2-21x-18$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-6)(x+3)(x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x-6x-18)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-3x-18)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+x^2-3x^2-3x-18x-18 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-2x^2-21x-18\end{aligned} $$ | |
| 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: $$ x^2+ \color{blue}{3x} \color{blue}{-6x} -18 = x^2 \color{blue}{-3x} -18 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-3x-18}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2-3x-18}\right) \cdot \left( x+1\right) = x^3+x^2-3x^2-3x-18x-18 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{x^2} \color{blue}{-3x^2} \color{red}{-3x} \color{red}{-18x} -18 = x^3 \color{blue}{-2x^2} \color{red}{-21x} -18 $$ |
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