Ta có:

`(4-a^2)(4-b^2)`

`= 16 - 4 (a^2 + b^2) + a^2b^2`

`= 4 [4 - (a^2 + b^2)] + a^2b^2`

`= 4 . (a^2 + b^2 + c^2 + abc - a^2 - b^2) + a^2b^2`

`= 4 (c^2 + abc) + a^2b^2`

`= a^2b^2 + 4abc + 4c^2`

`= (ab)^2 + 2 . ab . 2c + (2c)^2`

`= (ab+2c)^2`

Suy ra: `c sqrt((4-a^2)(4-b^2)) = c . sqrt((ab+2c)^2) = c . |ab + 2c| = c . (ab+2c)= abc + 2c^2`

Tương tự, ta có `{(a sqrt((4-b^2)(4-c^2)) = abc + 2a^2),(bsqrt((4-c^2)(4-a^2)) = abc + 2b^2):}`

Do đó: `P = abc + 2a^2 + abc + 2b^2 + abc + 2c^2 - abc = 2 (a^2+b^2+c^2+abc) = 2.4 = 8`