Question:
Find the value
$2(x+y)^{2}-9(x+y)-5$
Solution:
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)
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