Factorize : \( \frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x \)
\[
\frac{8}{27}x^3 + 1 + \frac{4}{3}x^2 + 2x
\]
\[
= \frac{8}{27}x^3 + \frac{4}{3}x^2 + 2x + 1
\]
\[
= \left(\frac{2x}{3}\right)^3
+ 3\left(\frac{2x}{3}\right)^2(1)
+ 3\left(\frac{2x}{3}\right)(1)^2
+ 1^3
\]
\[
= \left(\frac{2x}{3} + 1\right)^3
\]