Question

Factorize:
$x^2+\frac{2}{3}x+\frac{1}{9}$

Answer 1

$x^2+\frac{2}{3}x+\frac{1}{9}$

$=x^2+\frac{1}{3}x+\frac{1}{3}x+\frac{1}{9}$

$=x\left(x+\frac{1}{3}\right)+\frac{1}{3}\left(x+\frac{1}{3}\right)$

$=\left(x+\frac{1}{3}\right)\left(x+\frac{1}{3}\right)$

$={\left(x+\frac{1}{3}\right)}^2.$

Hence, the answer is ${\left(x+\frac{1}{3}\right)}^2.$