Answer
$$x(x+1)(2x+1)-3x^2-3x=2x^3-2x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x+1)(2x+1)-3x^2-3x& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+x)(2x+1)-3x^2-3x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^3+x^2+2x^2+x-3x^2-3x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3-2x\end{aligned} $$ | |
| 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( 2x+1\right) $. $$ \left( \color{blue}{x^2+x}\right) \cdot \left( 2x+1\right) = 2x^3+x^2+2x^2+x $$ |
| ③ | Combine like terms: $$ 2x^3+ \color{blue}{x^2} + \color{red}{2x^2} + \color{green}{x} \color{red}{-3x^2} \color{green}{-3x} = 2x^3 \color{green}{-2x} $$ |
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