Factorise the following:
$x^{2} + 9 x y + 18 y^{2}$

(x + 3 y) (x - y)

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(x - 3 y) (x - 6 y)

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(x - 3 y) (2 x + y)

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(x + 3 y) (x + 6 y)

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Solution

The correct option is D $(x + 3 y) (x + 6 y)$
$x^{2} + 9 x y + 18 y^{2}$
$= x^{2} + 6 x y + 3 x y + 18 y^{2}$
$= x (x + 6 y) + 3 y (x + 6 y)$
$= (x + 6 y) (x + 3 y)$

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$(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =$

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2} =

(2 x - 3 y)^{3} + (x + 3 y)^{3} + 3 (2 x - 3 y)^{2} (x + 3 y) + 3 (2 x - 3 y) (x + 3 y)^{2}

2 x^{2} - 18 y^{2}

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