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