Calcul MENTAL: a) Factoriser (x+1)^2 - (x-1)^2 b) Calculer 10001^2 - 9999^2
Mathématiques
1DACADEMIE
Question
Calcul MENTAL:
a) Factoriser (x+1)^2 - (x-1)^2
b) Calculer 10001^2 - 9999^2
a) Factoriser (x+1)^2 - (x-1)^2
b) Calculer 10001^2 - 9999^2
1 Réponse
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1. Réponse Anonyme
(x + 1)² - (x - 1)²
= x² + 2x + 1 - (x² - 2x + 1)
= x² + 2x + 1 - x² + 2x - 1
= 4x
10 001² - 9 999²
= (10 000 + 1)² - (10 000 - 1)²
= 10 000² + 20 000 + 1 - (10 000² - 20 000 + 1)
= 10 000² + 20 000 + 1 - 10 000² + 20 000 - 1
= 20 000 + 20 000
= 40 000