Factorise the following:
$(y^{2} + 5 y) (y^{2} + 5 y - 2) - 24$

(y - 1) (y + 3) (y + 7) (y - 1)

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(y + 1) (y + 4) (y + 6) (y - 1)

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(y + 1) (y - 4) (y + 6) (y + 1)

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(y - 1) (2 y + 4) (y + 6) (2 y - 1)

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Solution

The correct option is B $(y + 1) (y + 4) (y + 6) (y - 1)$
$(y^{2} + 5 y) (y^{2} + 5 y - 2) - 24$
Let $(y^{2} + 5 y)$ be $a$
$a (a - 2) - 24$
$= a^{2} - 2 a - 24$
$= a^{2} - 6 a + 4 a - 24$
$= a (a - 6) + 4 (a - 6)$
$= (a - 6) (a + 4)$
Resubstituting the value we get,
$(y^{2} + 5 y - 6) (y^{2} + 5 y + 4)$
$= (y^{2} + 6 y - y - 6) (y^{2} + 4 y + y + 4)$
$= [y (y + 6) - 1 (y + 6)] [y (y + 4) + 1 (y + 4)]$
$= (y + 6) (y - 1) (y + 4) (y + 1)$

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