Question
Factorise the following, using the identity $a^2+ 2ab + b^2= (a + b)^2$
$9\text{x}^2+2\text{xy}+\frac{\text{y}^2}{9}$
$9\text{x}^2+2\text{xy}+\frac{\text{y}^2}{9}$
✓
Answer
$9\text{x}^2+2\text{xy}+\frac{\text{y}^2}{9}$$=(3\text{x})^2+2\times3\text{x}\times\frac{\text{y}}{3}+\Big(\frac{\text{y}}{3}\Big)^2$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)^2$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)\Big(3\text{x}+\frac{\text{y}}{3}\Big)$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)^2$
$=\Big(3\text{x}+\frac{\text{y}}{3}\Big)\Big(3\text{x}+\frac{\text{y}}{3}\Big)$
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