Réponse :

bonjour,

1-

AD = (x + 3)+(x-2) = x + 3 + x - 2 = 2x + 1

Aire ABCD = (2x + 1)²

Aire ABEF = (2x + 1 )×( x + 3 )

Aire ECDF = (2x + 1 )×( x - 2 ) = 2x² - 4x + x - 2 = 2x² - 3x - 2

2-

Aire ABEF ( B ) = (2x + 1 )×( x + 3 ) = 2x² + 6x + x + 3 = 2x² + 7x + 3

Aire ECDF ( C ) = (2x + 1 )×( x - 2 ) = 2x² - 4x + x - 2 = 2x² - 3x - 2

(2x² +  7x + 3 ) + ( 2x² - 3x - 2 )

= 2x² +  7x + 3  + 2x² - 3x - 2

Aire ABEF + Aire ECDF = 4x² + 4x + 1

Aire ABCD = (2x + 1)²

d'apres l'identité remarquable (a+b)² = a² + 2ab + b²

= (2x)² + 2×2x×1 + 1²

= 4x² + 4x + 1

Aire ABCD = Aire ABEF + Aire ECDF

voila :)