Question
Answer
$$(x+2)(x+3)(x+1)=x^3+6x^2+11x+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2)(x+3)(x+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+3x+2x+6)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+5x+6)(x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3+x^2+5x^2+5x+6x+6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+6x^2+11x+6\end{aligned} $$ | |
| 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: $$ x^2+ \color{blue}{3x} + \color{blue}{2x} +6 = x^2+ \color{blue}{5x} +6 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+5x+6}\right) $ by each term in $ \left( x+1\right) $. $$ \left( \color{blue}{x^2+5x+6}\right) \cdot \left( x+1\right) = x^3+x^2+5x^2+5x+6x+6 $$ |
| ④ | Combine like terms: $$ x^3+ \color{blue}{x^2} + \color{blue}{5x^2} + \color{red}{5x} + \color{red}{6x} +6 = x^3+ \color{blue}{6x^2} + \color{red}{11x} +6 $$ |
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