Resolve the following quadratic trinomial into factors:

$15 x^{2} - 16 x y z - 15 y^{2} z^{2}$

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Solution

Given: $15 x^{2} - 16 x y z - 15 y^{2} z^{2}$

On splitting the middle term, we get

$15 x^{2} - 25 x y z + 9 x y z - 15 y^{2} z^{2}$

$= 5 x (3 x - 5 y z) + 3 y z (3 x - 5 y z)$

$= (5 x + 3 y z) (3 x - 5 y z)$

$∴ 15 x^{2} - 16 x y z - 15 y^{2} z^{2} = (5 x + 3 y z) (3 x - 5 y z)$

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