Resolve the following quadratic trinomial into factors :
$14 x^{2} + 11 x y - 15 y^{2}$

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Solution

Given : $14 x^{2} + 11 x y - 15 y^{2}$
On splitting the middle term, we get
$14 x^{2} + 21 x y - 10 x y - 15 y^{2}$
$= 7 x (2 x + 3 y) - 5 y (2 x + 3 y)$
$= (2 x + 3 y) (7 x - 5 y)$

Hence, $14 x^{2} + 11 x y - 15 y^{2} = (2 x + 3 y) (7 x - 5 y)$ .

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