Question

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

• A. $(a-\frac{1}{a}{)}^2$
• B. $(a-\frac{2}{a}{)}^2$
• C. $(a+\frac{1}{a}{)}^2$
• D. $(a-\frac{1}{2a}{)}^2$

Answer 1

The correct option is A $(a-\frac{1}{a}{)}^2$

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