Bonsoir,
A = (6x + 5)² - (6x + 5)(7x + 2)
1. Développer l'expression A :
A = (6x + 5)² - (6x + 5)(7x + 2)
>> identité remarquable :
A = (6x)² + 2*6x*5 + 5² - (6x + 5)(7x + 2)
A = 36x² + 60x + 25 - (6x + 5)(7x + 2)
>> double distributivité :
- (a + b)(c + d) = ac + ad + bc + bd
A = 36x² + 60x + 25 - (42x² + 12x + 35x + 10)
A = 36x² + 60x + 25 - (42x² + 47x + 10)
A = 36x² + 60x + 25 - 42x² - 47x - 10
A = -6x² + 13x + 15 ✅
2. Développer l'expression A :
A = (6x + 5)² - (6x + 5)(7x + 2)
>> on met en évidence le facteur commun :
A = (6x + 5)(6x + 5) - (6x + 5)(7x + 2)
>> On factorise :
A = (6x + 5)(6x + 5 - (7x + 2))
A = (6x + 5)(6x + 5 - 7x - 2)
A = (6x + 5)(3 - x) ✅
* = multiplication
Bonne soirée
