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