Factorise $15 (2 x - y)^{2} - 16 (2 x - y) - 15)$

$(10 x - 5 y + 2) (10 x - 5 y - 2)$

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$(10 x - 5 y) (10 x + 5 y)$

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$(10 x - 5 y + 3) (10 x - 5 y - 5)$

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$(5 y + 3) (5 y - 5)$

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Solution

The correct option is C
$(10 x - 5 y + 3) (10 x - 5 y - 5)$

Given $15 (2 x - y)^{2} - 16 (2 x - y) - 15)$
Taking $(2 x - y)$ as $a$ , we have

$15 (2 x - y)^{2} - 16 (2 x - y) - 15)$
= $15 a^{2} - 16 a - 15$
= $15 a^{2} - 25 a + 9 a - 15$
= $5 a (3 a - 5) + 3 (3 a - 5)$
= $(5 a + 3) (3 a - 5)$
Subsituting $a = 2 x - y$ , we have
= $(5 (2 x - y) + 3) (3 (2 x - y) - 5)$
= $(10 x - 5 y + 3) (10 x - 5 y - 5)$

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