Salut,
1) pour a = 1 et b = 5 on a :
A = 1/4 [ ( 1 + 5)² - (1 - 5)² ] = 1/4 [ 6² - ( - 4)² ] = 1/4 [ 36 - 16 ] = 1/4 [ 20 ] = 20/4 = 5.
2) pour a = - 2 et b = -3 on a :
A = 1/4 [ ( - 2 - 3)² - ( - 2 - ( - 3))² ] = 1/4 [ ( - 5 )² - ( 1 )² ] = 1/4 [ 25 - 1 ] = 1/4 [24] = 24/4 = 6.
3) A = 1/4 [ ( a + b )² - ( a - b )² ]
= 1/4 [ ( a + b + a - b )( a + b - a + b) ]
= 1/4 [ ( 2a )( 2b )]
= 1/4 [ 4ab ] = ab.
on a ppliqué l'identité remarquable (a+b)(a-b)=a² - b².
