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