Factorise Completely : $x^{2} + 6 x y + 9 y^{2} + x + 3 y$

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Solution

$x^{2} + 6 x y + 9 y^{2} + x + 3 y = [(x)^{2} + 2 \times x \times 3 y + (3 y)^{2}] + (x + 3 y) = [x + 3 y]^{2} + (x + 3 y) = (x + 3 y) (x + 3 y) + (x + 3 y) = (x + 3 y) (x + 3 y + 1)$

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