Explique comment calculer mentalement 9 996² - 9 998 *(foix) 9 992 (URGEEENT) ! =)

9996²-9998*9992=
(x-4)²-(x-2)(x-8) =
x²-8x+16-x²+8x+2x-16 =
2x
x = 10 000
(10 000-4)-(10 000-2)(10 000-8) = 2x =
2*10 000 = 20 000

A = ( 9996 )² - ( 9998 ) * ( 9992 )

On remarque que :
99996 = 10 000 - 4
9998 = 10 000 - 2
9992 = 10 000 - 8

Donc :

A = (10 000 - 4)² - ((10 000 - 2)  (10 000 - 8)

si x = 10 000
A = (x - 4)² - ((x - 2)  (x - 8)
A = x² - 8x + 16 - ( x² - 2x - 8x + 16)
A = x² - 8x + 16 - x² +  2x + 8x - 16
A =  2x


Donc

A = (10 000 - 4)² - ((10 000 - 2)  (10 000 - 8)
A = 2(10 000)
A = 20 000