Factorise : $9 x^{2} + 4 y^{2} + 1 + 12 x y + 4 y + 6 x$

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Solution

Now,
$9 x^{2} + 4 y^{2} + 1 + 12 x y + 4 y + 6 x$
$= 9 x^{2} + 12 x y + 4 y^{2} + 1 + 2 (2 y + 3 x)$
$= (3 x + 2 y)^{2} + 2 (3 x + 2 y) + 1$
$= (3 x + 2 y + 1)^{2}$ .

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