Question
Answer
$$(x+5+6.8i)(x+5-6.8i)(x+25)=-36i^2x+x^3-900i^2+35x^2+275x+625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5+6.8i)(x+5-6.8i)(x+25)& \xlongequal{ }(x+5+6i)(x+5-6i)(x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(-36i^2+x^2+10x+25)(x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-36i^2x+x^3-900i^2+35x^2+275x+625\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+5+6i}\right) $ by each term in $ \left( x+5-6i\right) $. $$ \left( \color{blue}{x+5+6i}\right) \cdot \left( x+5-6i\right) = \\ = x^2+5x -\cancel{6ix}+5x+25 -\cancel{30i}+ \cancel{6ix}+ \cancel{30i}-36i^2 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{5x} \, \color{red}{ -\cancel{6ix}} \,+ \color{blue}{5x} +25 \, \color{orange}{ -\cancel{30i}} \,+ \, \color{red}{ \cancel{6ix}} \,+ \, \color{orange}{ \cancel{30i}} \,-36i^2 = -36i^2+x^2+ \color{blue}{10x} +25 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{-36i^2+x^2+10x+25}\right) $ by each term in $ \left( x+25\right) $. $$ \left( \color{blue}{-36i^2+x^2+10x+25}\right) \cdot \left( x+25\right) = -36i^2x-900i^2+x^3+25x^2+10x^2+250x+25x+625 $$ |
| ④ | Combine like terms: $$ -36i^2x-900i^2+x^3+ \color{blue}{25x^2} + \color{blue}{10x^2} + \color{red}{250x} + \color{red}{25x} +625 = -36i^2x+x^3-900i^2+ \color{blue}{35x^2} + \color{red}{275x} +625 $$ |
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