Question
Expand the following, using suitable identities.$\Big(\frac{2\text{x}}{3}-\frac{2}{3}\Big)\Big(\frac{2\text{x}}{3}+\frac{2\text{a}}{3}\Big)$
✓
Answer
$\Big(\frac{2\text{x}}{3}-\frac{2}{3}\Big)\Big(\frac{2\text{x}}{3}+\frac{2\text{a}}{3}\Big)$$=\Big(\frac{2\text{x}}{3}\Big)^2+\Big(-\frac{2}{3}+\frac{2\text{a}}{3}\Big)+\Big(-\frac{2}{3}+\frac{2\text{a}}{3}\Big)\frac{2\text{x}}{3}+\Big(-\frac{2}{3}\times\frac{2\text{a}}{3}\Big)$
$=\frac{4\text{x}^2}{9}+\frac{2\text{a}-2}{3}\times\frac{2}{3}\text{x}-\frac{4}{9}\text{a}$
$=\frac{4\text{x}^2}{9}+\frac{4}{9}(\text{a}-1)\text{x}-\frac{4}{9}\text{a}$
$=\frac{4\text{x}^2}{9}+\frac{2\text{a}-2}{3}\times\frac{2}{3}\text{x}-\frac{4}{9}\text{a}$
$=\frac{4\text{x}^2}{9}+\frac{4}{9}(\text{a}-1)\text{x}-\frac{4}{9}\text{a}$
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