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