Réponse :
51² = (50 + 1)² = 50² + 2x50 + 1² = 2500 + 100 + 1 = 2501
99² = (100 - 1)² = 100² - 200 + 1² = 10001 - 200 = 9801
29² = (30 - 1)² = 901 - 60 = 841
31² = (30 + 1)² = 901 + 60 = 961
29 * 31 = (30 + 1) * (30 - 1) = 30² - 1² = 900 - 1 = 899
202² = (200 + 2)² =40004 + 800 = 40804
999² = (1000 - 1)² = 1000001 - 2000 = 998001
98² = (100 - 2)² = 10004 - 400 = 9604
ou si a² - b² = (a+b)*(a-b) alors a² = (a+b)*(a-b) + b² --> 98*98 = 96 * 100 + 2*2
202 x 198 = (200 + 2) (200 - 2) = 40000 - 4 = 39996
105² = 100 * 110 + 5² = 11025
ou encore (Xu)² avec X multiple de 10 --> X*(X+1) = 10*11 = 110 et u² = 25
47 * 53 = 50² - 3² = 2500 - 9 = 2500 - 10 + 1 = 2491
65*75 = 70² - 5² = 4900 - 25 = 4875
autre exemple
65² = (du)² --> d*d+1 = 6*7=42 et u² = 25
65² = 4225 = 60*70 + 5² = 4200 + 25 = 4225
Explications étape par étape
