Question

Factorize: $36a^2-12+\frac{1}{a^2}$

• A. $(a-\frac{1}{6a}{)}^2$
• B. $(6a-\frac{1}{6a}{)}^2$
• C. $(6a-\frac{1}{a}{)}^2$
• D. $(6a-\frac{6}{a}{)}^2$

Answer 1

The correct option is C $(6a-\frac{1}{a}{)}^2$

$\Rightarrow 36a^2-12+\frac{1}{a^2}$

$\Rightarrow (6a{)}^2-2\times (6a)\frac{1}{a}+(\frac{1}{a}{)}^2$

$\Rightarrow (6a{)}^2-(6a)\frac{1}{a}-(6a)\frac{1}{a}+(\frac{1}{a}{)}^2$

$\Rightarrow 6a(6a-\frac{1}{a})-\frac{1}{a}(6a-\frac{1}{a})$

$\Rightarrow (6a-\frac{1}{a})(6a-\frac{1}{a})$

$\Rightarrow (6a-\frac{1}{a}{)}^2$