Answer
$$(5-2xi)\cdot(5-3i)-(5-2xi)\cdot(5+1)=6i^2x+2ix-15i-5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5-2xi)\cdot(5-3i)-(5-2xi)\cdot(5+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(5-2xi)\cdot(5-3i)-(5-2xi)\cdot6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}25-15i-10ix+6i^2x-(30-12ix) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}25-15i-10ix+6i^2x-30+12ix \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6i^2x+2ix-15i-5\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{5} + \color{blue}{1} = \color{blue}{6} $$ |
| ② | Multiply each term of $ \left( \color{blue}{5-2ix}\right) $ by each term in $ \left( 5-3i\right) $. $$ \left( \color{blue}{5-2ix}\right) \cdot \left( 5-3i\right) = 25-15i-10ix+6i^2x $$$$ \left( \color{blue}{5-2ix}\right) \cdot 6 = 30-12ix $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 30-12ix \right) = -30+12ix $$ |
| ④ | Combine like terms: $$ \color{blue}{25} -15i \color{red}{-10ix} +6i^2x \color{blue}{-30} + \color{red}{12ix} = 6i^2x+ \color{red}{2ix} -15i \color{blue}{-5} $$ |
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