Bonsoir,
On considère l'expression :
A = (2x + 1)² - (x - 3)(2x + 1)
1. Développer et réduire A.
A = (2x + 1)² - (x - 3)(2x + 1)
A = 4x² + 4x + 1 - (2x² + x - 6x - 3)
A = 4x² + 4x + 1 - 2x² - x + 6x + 3
A = 4x² - 2x² + 4x + 6x - x + 1 + 3
A = 2x² + 9x + 4
2.Factoriser A.
A = (2x + 1)² - (x - 3)(2x + 1)
A = (2x + 1) [(2x + 1) - (x - 3)]
A = (2x + 1) (2x + 1 - x + 3)
A = (2x + 1) (x + 4)
3.Calculer A pour x= - 1/2
A = 2x² + 9x + 4
A = 2 * - 1/2² + 9 * - 1/2 + 4
A = 2 * 1/4 - 9/2 + 4
A = 2/4 - 9/2 + 4
A = 1/2 - 9/2 + 8/2
A = 0
