Question

Find the factors of a^2+1/a^2+2-2a-2/a

Answer 1

★To find :

$factors \:of \:a^2 + \frac{1}{a^2} +2-2a - \frac{2}{a}$

★Solution:

$We \:know\:that \\ \\ \\ (a+b)^2 = a^2+b^2+2ab\\ \\ \\ \left(a+\frac{1}{a}\right)^2 = a^2+\frac{1}{a^2}+ 2 \left(a \times \frac{1}{a}\right)$

$= a^2+\frac{1}{a^2}+2 \\ \\ \\ \therefore \:a^2 + \frac{1}{a^2} +2-2a - \frac{2}{a}$

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

$= (a+\frac{1}{a})^2 -2\left(a + \frac{1}{a}\right)$

$by\:taking\:a+\frac{1}{a} \:common\\ \\ \\ \left(a+\frac{1}{a}\right) \left(a+\frac{1}{a} -2\right)\\ \\ \\ \therefore \:the\:factors\:are \: \left(a+\frac{1}{a}\right) \:and \:\left(a+\frac{1}{a} -2\right)$

Answer 2

x²- 1 - 2a - a²

= x²- (a²+ 2a + 1)

= x²- (a + 1)²

= (x+a+1) (x - a -1)

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