Question

Factorize $\frac{8}{27}{x}^3+1+\frac{4}{3}{x}^2+2x$

Answer 1

$\frac{8}{27}{x}^3+1+\frac{4}{3}{x}^2+2x={\left(\frac{2}{3}x\right)}^3+(1{)}^3+3\times {\left(\frac{2}{3}x\right)}^2\times 1+3\times \frac{2}{3}x\times (1{)}^2={(\frac{2}{3}x+1)}^3=(\frac{2}{3}x+1)(\frac{2}{3}x+1)(\frac{2}{3}x+1)$