Explications étape par étape:
48) Factorisation via la 3ème identité remarquable :
a. (5x + 1)² - 81 = (5x + 1 - 9)(5x + 1 + 9) = (5x - 8)(5x + 10)
b. (7d + 2)² - (3d + 4)² = (7d + 2 - 3d - 4)(7d + 2 + 3d + 4) = (4d - 2)(10d + 6)
49) Factorisation via la 3ème identité remarquable
a. 105² - 95² = (105 - 95)(105 + 95) = 10 × 200 = 2000
b. 1001² - 1000² = (1001 - 1000)(1001 + 1000) = 1 × 2001 = 2001
c. 2008² - 8² = (2008 - 8)(2008 + 8) = 2000 × 2016 = 2016 × 2 × 1000 = 4032 × 1000 = 4032000
d. 573² - 572² = (573 - 572)(573 + 572) = 1 × (500 + 500 + 70 + 70 + 3 + 3) = 1000 + 140 + 6 = 1146
