Factorise the following by using suitable identity
$x^{2} + 6 x y + 9 y^{2}$

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Solution

$x^{2} + 6 x y + 9 y^{2}$
$= (x)^{2} + 2. x .3 y + (3 y)^{2}$
$= (x + 3 y)^{2}$ $∵ (a + b)^{2} = a^{2} + 2 a b + b^{2}$
$= (x + 3 y) (x + 3 y)$

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