Réponse :
Explications étape par étape :
Bonjour,
A(x) = x² + 2x = x(x+2)
B(x) = 7x(x-4) + (x-4) = (x-4) (7x+1)
C(x) = (x+1)(2x+5) - (x+1)(3x+4) = (x+1)(2x+5-3x-4) = (x+1) (1-x)
D(u) = 9u² + 3u = 3u(3u+1)
E(t) = (2-t)(3t+1) + (3t+1)(2t) = (3t+1) (2-t+2t) = (3t+1) (2+t)
F(u) = (u-1)(3u+4) - (1-u)(2u+3) = (u-1) (3u+4+2u+3) = (u-1) (5u+7)
Exercice 7 :
On va essayer de ce ramener à des nombres dont les opérations sont faciles a calculer de tête :
D = 48 x 99 = 48 x (100-1) = 48 x 100 - 48 = 4800 - 48 = 4752
ou 48 x 100 - (50-2) = 4800 -50 +2 = 4750 +2 = 4752
E = 57 x 101 = 57 x (100+1) = 57 x 100 + 57 = 5700 + 57 = 5757
F = 101² = 101 x (100+1 ) = 101 x 100 + 101 = 10100 +101 = 10201
ou (100+1)(100+1) = 100² +2x100 +1² = 10000 + 200 + 1 10201 (identité remarquable)
G = 23 x 11 = 23 x (10+1) = 23 x 10 + 23 = 230 +23 = 253
