$a-b=\sqrt {22+12\sqrt {2}}-3\sqrt {2} $
$a-b=\sqrt {4+2.2.3\sqrt {2}+18}-3\sqrt {2} $
$a-b=\sqrt {(2+3\sqrt {2})^{2}}-3\sqrt {2} $
$a-b=2+3\sqrt {2}-3\sqrt {2} $
$a-b=2$
Ta có:
$P=(a+b+1)^{2}-2a-2b-4ab $
$P=a^{2}+b^{2}+1+2ab+2a+2b-2a-2b-4ab $
$P=a^{2}-2ab+b^{2}+1$
$P=(a-b)^{2}+1$
$P=2^{2}+1$
$P=5$
Vậy với $a-b=\sqrt {22+12\sqrt {2}}-3\sqrt {2} $ thì $P=5$