Answer
$$x(2x+1)(2x+1)(x-4)=4x^4-12x^3-15x^2-4x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(2x+1)(2x+1)(x-4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2x^2+x)(2x+1)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(4x^3+2x^2+2x^2+x)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(4x^3+4x^2+x)(x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^4-16x^3+4x^3-16x^2+x^2-4x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^4-12x^3-15x^2-4x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( 2x+1\right) $ $$ \color{blue}{x} \cdot \left( 2x+1\right) = 2x^2+x $$ |
| ② | Multiply each term of $ \left( \color{blue}{2x^2+x}\right) $ by each term in $ \left( 2x+1\right) $. $$ \left( \color{blue}{2x^2+x}\right) \cdot \left( 2x+1\right) = 4x^3+2x^2+2x^2+x $$ |
| ③ | Combine like terms: $$ 4x^3+ \color{blue}{2x^2} + \color{blue}{2x^2} +x = 4x^3+ \color{blue}{4x^2} +x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{4x^3+4x^2+x}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{4x^3+4x^2+x}\right) \cdot \left( x-4\right) = 4x^4-16x^3+4x^3-16x^2+x^2-4x $$ |
| ⑤ | Combine like terms: $$ 4x^4 \color{blue}{-16x^3} + \color{blue}{4x^3} \color{red}{-16x^2} + \color{red}{x^2} -4x = 4x^4 \color{blue}{-12x^3} \color{red}{-15x^2} -4x $$ |
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