Question
Answer
$$(i+sqrt\cdot5)(sqrt-4+1)=5q^2r^2s^2t^2+iqrst-15qrst-3i$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(i+sqrt\cdot5)(sqrt-4+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(i+sqrt\cdot5)(1qrst-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}iqrst-3i+5q^2r^2s^2t^2-15qrst \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5q^2r^2s^2t^2+iqrst-15qrst-3i\end{aligned} $$ | |
| ① | Combine like terms: $$ qrst \color{blue}{-4} + \color{blue}{1} = qrst \color{blue}{-3} $$ |
| ② | Multiply each term of $ \left( \color{blue}{i+5qrst}\right) $ by each term in $ \left( qrst-3\right) $. $$ \left( \color{blue}{i+5qrst}\right) \cdot \left( qrst-3\right) = iqrst-3i+5q^2r^2s^2t^2-15qrst $$ |
| ③ | Combine like terms: $$ 5q^2r^2s^2t^2+iqrst-15qrst-3i = 5q^2r^2s^2t^2+iqrst-15qrst-3i $$ |
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