Factorise the following:
$x^{2} + 8 x + 24 y - 9 y^{2}$

(x + y) (x - 3 y + 8)

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(x + 3 y) (x - 3 y + 8)

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(x + 2 y) (x - 3 y + 8)

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(2 x + 3 y) (x - 3 y + 8)

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Solution

The correct option is B $(x + 3 y) (x - 3 y + 8)$
$x^{2} + 8 x + 24 y - 9 y^{2}$
$= x^{2} - 9 y^{2} + 8 x + 24 y$
$= (x - 3 y) (x + 3 y) + 8 (x + 3 y)$
$= (x + 3 y) (x - 3 y + 8)$

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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} =

9 x^{2} - 9 y^{2} = 8

y^{2} = 32 x

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