Question 85 (viii)

Expand the following, using suitable identities.

$(\frac{4 x}{5} + \frac{y}{4}) (\frac{4 x}{5} + \frac{3 y}{4})$

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Solution

We have,
$(\frac{4 x}{5} + \frac{y}{4}) (\frac{4 x}{5} + \frac{3 y}{4}) = {(\frac{4 x}{5})}^{2} + (\frac{y}{4} + \frac{3 y}{4}) \frac{4 x}{5} + \frac{y}{4} \times \frac{3 y}{4}$ [using the identity, $(x + a) (x + b) = x^{2} + (a + b) x + a b$ ]
$= \frac{16}{25} x^{2} + \frac{4 x y}{5} + \frac{3 y^{2}}{16}$

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