Question 85 (xi)

Expand the following, using suitable identities.

$(\frac{2 a}{3} + \frac{b}{3}) (\frac{2 a}{3} - \frac{b}{3})$

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Solution

We have,
$(\frac{2 a}{3} + \frac{b}{3}) (\frac{2 a}{3} - \frac{b}{3}) = {(\frac{2 a}{3})}^{2} - {(\frac{b}{3})}^{2}$
[using the identity, $(a + b) (a - b) = a^{2} - b^{2}$ ]
$= \frac{4}{9} a^{2} - \frac{1}{9} b^{2}$

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Expand the following, using suitable identities.

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