Question
Answer
$$x(x+1)(x+2)(x+3)=x^4+6x^3+11x^2+6x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x+1)(x+2)(x+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x)(x+2)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+2x^2+x^2+2x)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3+3x^2+2x)(x+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4+3x^3+3x^3+9x^2+2x^2+6x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^4+6x^3+11x^2+6x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x+1\right) $ $$ \color{blue}{x} \cdot \left( x+1\right) = x^2+x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2+x}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x^2+x}\right) \cdot \left( x+2\right) = x^3+2x^2+x^2+2x $$ |
| ③ | Combine like terms: $$ x^3+ \color{blue}{2x^2} + \color{blue}{x^2} +2x = x^3+ \color{blue}{3x^2} +2x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3+3x^2+2x}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{x^3+3x^2+2x}\right) \cdot \left( x+3\right) = x^4+3x^3+3x^3+9x^2+2x^2+6x $$ |
| ⑤ | Combine like terms: $$ x^4+ \color{blue}{3x^3} + \color{blue}{3x^3} + \color{red}{9x^2} + \color{red}{2x^2} +6x = x^4+ \color{blue}{6x^3} + \color{red}{11x^2} +6x $$ |
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