Question
Answer
$$(x-2)(x-5i)(x+5i)=-25i^2x+x^3+50i^2-2x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x-5i)(x+5i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-5ix-2x+10i)(x+5i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-25i^2x+x^3+50i^2-2x^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x-5i\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x-5i\right) = x^2-5ix-2x+10i $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-5ix-2x+10i}\right) $ by each term in $ \left( x+5i\right) $. $$ \left( \color{blue}{x^2-5ix-2x+10i}\right) \cdot \left( x+5i\right) = \\ = x^3+ \cancel{5ix^2} -\cancel{5ix^2}-25i^2x-2x^2 -\cancel{10ix}+ \cancel{10ix}+50i^2 $$ |
| ③ | Combine like terms: $$ x^3+ \, \color{blue}{ \cancel{5ix^2}} \, \, \color{blue}{ -\cancel{5ix^2}} \,-25i^2x-2x^2 \, \color{green}{ -\cancel{10ix}} \,+ \, \color{green}{ \cancel{10ix}} \,+50i^2 = -25i^2x+x^3+50i^2-2x^2 $$ |
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