Factorise the following by splitting the middle terms:

g) $15 a^{2} - 14 a - 16$

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Solution

Given: $15 a^{2} - 14 a - 16$
By splitting the middle term, we get,
$= 15 a^{2} + 10 a - 24 a - 16$
$= 5 a (3 a + 2) - 8 (3 a + 2)$
$= (3 a + 2) (5 a - 8)$
Hence, the answer is $(5 a - 8) (3 a + 2)$ .

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