Question

Factorize: $7a^2+14+\frac{7}{a^2}$

• A. $7(a+\frac{7}{a}{)}^2$
• B. $(a+\frac{1}{a}{)}^2$
• C. $49(a+\frac{1}{a}{)}^2$
• D. $7(a+\frac{1}{a}{)}^2$

Answer 1

The correct option is D $7(a+\frac{1}{a}{)}^2$

$\Rightarrow 7a^2+14+\frac{7}{a^2}$

$\Rightarrow 7(a^2+2+\frac{1}{a^2})$

$\Rightarrow 7(a^2+\frac{a}{a}+\frac{a}{a}+\frac{1}{a^2})$

$\Rightarrow 7\left[a\right(a+\frac{1}{a})+\frac{1}{a}(a+\frac{1}{a}\left)\right]$

$\Rightarrow 7(a+\frac{1}{a})(a+\frac{1}{a})$

$\Rightarrow 7(a+\frac{1}{a}{)}^2$