Find the value

Let $x+y=z$

$=2 z^{2}-9 z-5$

Splitting the middle term,

$=2 z^{2}-10 z+z-5$

$=2 z(z-5)+1(z-5)$

$=(z-5)(2 z+1)$

Substituting z = x + y

= (x + y − 5)(2(x + y) + 1)

= (x + y − 5)(2x + 2y + 1)

∴ 2(x + y)2 − 9(x + y) − 5 = (x + y − 5)(2x + 2y + 1)