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