Question

Factorise: x 2 + 1/x 2 + 2 - 2x - 2/x

Answer 1

Answer:

$x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}\\=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)$

Step-by-step explanation:

$Given ,\\x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}$

$=x^{2}+\frac{1}{x^{2}}+2\times x \times \frac{1}{x}-2x-\frac{2}{x}$

$=\big(x+\frac{1}{x}\big)^{2}-2\big(x+\frac{1}{x}\big)$

$=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)$

Therefore,

$x^{2}+\frac{1}{x^{2}}+2-2x-\frac{2}{x}\\=\big(x+\frac{1}{x}\big)\big(x+\frac{1}{x}-2\big)$

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Answer 2

Hope it helps!

Answer

Explanation