Question
Factorize:
$\frac{8}{27}\text{x}^3+1+\frac{4}{3}\text{x}^2+2\text{x}$
$\frac{8}{27}\text{x}^3+1+\frac{4}{3}\text{x}^2+2\text{x}$
✓
Answer
$\frac{8}{27}\text{x}^3+1+\frac{4}{3}\text{x}^2+2\text{x}$
$=\Big(\frac{2}{3}\text{x}\Big)^3+(1)^3+3\times\Big(\frac{2}{3}\text{x}\Big)^2\times1+3(1)^2\times\Big(\frac{2}{3}\text{x}\Big)$
$=\Big(\frac{2}{3}\text{x}+1\Big)^3$$\big[\because$ a3 + b3 + 3a2b + 3ab2 = (a + b)3$\big]$
$=\Big(\frac{2}{3}\text{x}+1\Big)\Big(\frac{2}{3}\text{x}+1\Big)\Big(\frac{2}{3}\text{x}+1\Big)$
$\therefore\frac{8}{27}\text{x}^3+1+\frac{4}{3}\text{x}^2+2\text{x}$
$=\Big(\frac{2}{3}\text{x}+1\Big)\Big(\frac{2}{3}\text{x}+1\Big)\Big(\frac{2}{3}\text{x}+1\Big)$
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