Answer
$$x(x-4)(x+4)(x-2)=x^4-2x^3-16x^2+32x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}x(x-4)(x+4)(x-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-4x)(x+4)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^3+4x^2-4x^2-16x)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^3-16x)(x-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-2x^3-16x^2+32x\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{x} $ by $ \left( x-4\right) $ $$ \color{blue}{x} \cdot \left( x-4\right) = x^2-4x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-4x}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x^2-4x}\right) \cdot \left( x+4\right) = x^3+ \cancel{4x^2} -\cancel{4x^2}-16x $$ |
| ③ | Combine like terms: $$ x^3+ \, \color{blue}{ \cancel{4x^2}} \, \, \color{blue}{ -\cancel{4x^2}} \,-16x = x^3-16x $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^3-16x}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x^3-16x}\right) \cdot \left( x-2\right) = x^4-2x^3-16x^2+32x $$ |
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