Question 90 (xii)

Factorise the following, using the identity, $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ .

$9 y^{2} - 4 x y + \frac{4 x^{2}}{9}$

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Solution

We have,
$9 y^{2} - 4 x y + \frac{4 x^{2}}{9} = (3 y)^{2} - 2.3 y . \frac{2}{3} x + {(\frac{2}{3} x)}^{2} = {(3 y - \frac{2}{3} x)}^{2} = (3 y - \frac{2 x}{3}) (3 y - \frac{2 x}{3})$

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