Question
Find the square of $5-x+\frac{2}{x}$
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Answer
$ \left(5-x+\frac{2}{x}\right)^2$
$=(5)^2+(-x)^2+\left(\frac{2}{x}\right)^2+2 \times 5 \times(-x)+2(-x) \times \frac{2}{x}+2 \times \frac{2}{x} \times 5$
$ =25+x^2+\frac{4}{x^2}-10 x-4+\frac{20}{x}$
$ =21+x^2+\frac{4}{x^2}-10 x+\frac{20}{x}$
$=(5)^2+(-x)^2+\left(\frac{2}{x}\right)^2+2 \times 5 \times(-x)+2(-x) \times \frac{2}{x}+2 \times \frac{2}{x} \times 5$
$ =25+x^2+\frac{4}{x^2}-10 x-4+\frac{20}{x}$
$ =21+x^2+\frac{4}{x^2}-10 x+\frac{20}{x}$
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