Question
Answer
$$(sqrtx+sqrty)(x-sqrtxy+y)=-q^2r^2s^2t^2x^2y-q^2r^2s^2t^2xy^2+qrstx^2+2qrstxy+qrsty^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(sqrtx+sqrty)(x-sqrtxy+y)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}qrstx^2-q^2r^2s^2t^2x^2y+qrstxy+qrstxy-q^2r^2s^2t^2xy^2+qrsty^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-q^2r^2s^2t^2x^2y-q^2r^2s^2t^2xy^2+qrstx^2+2qrstxy+qrsty^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{qrstx+qrsty}\right) $ by each term in $ \left( x-qrstxy+y\right) $. $$ \left( \color{blue}{qrstx+qrsty}\right) \cdot \left( x-qrstxy+y\right) = \\ = qrstx^2-q^2r^2s^2t^2x^2y+qrstxy+qrstxy-q^2r^2s^2t^2xy^2+qrsty^2 $$ |
| ② | Combine like terms: $$ qrstx^2-q^2r^2s^2t^2x^2y+ \color{blue}{qrstxy} + \color{blue}{qrstxy} -q^2r^2s^2t^2xy^2+qrsty^2 = \\ = -q^2r^2s^2t^2x^2y-q^2r^2s^2t^2xy^2+qrstx^2+ \color{blue}{2qrstxy} +qrsty^2 $$ |
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