Bonsoir,
Utiliser les identités remarquables pour y arriver.
Expression 1:
(5x + 5) (4x + 6) + 25x² + 50x + 25
= (5x + 5) (4x + 6) + (5x+5)²
= (5x+5) ( 4x+6 +5x+5)
= (5x+5) ( 9x +11)
Expression 2:
(4x + 2) (7x - 9) + 16x² - 4
= (4x+2) ( 7x-9) + ( 4x-2) (4x+2)
= (4x+2) ( 7x-9 +4x-2)
= (4x+2) ( 11x -11)
Bonsoir :)
Réponse en explications étape par étape :
- Question : Factoriser les expressions suivantes :
A = (5x + 5)(4x + 6) + 25x² + 50x + 25
A = (5x + 5)(4x + 6) + (5x)² + (2 * 5x * 5) + (5)²
A = (5x + 5)(4x + 6) + (5x + 5)²
A = (5x + 5)(4x + 6) + (5x + 5)(5x + 5)
A = (5x + 5)(4x + 6 + 5x + 5)
A = (5x + 5)(9x + 11)
A = 5(x + 1)(9x + 11)
B = (4x + 2)(7x - 9) + 16x² - 4
B = (4x + 2)(7x - 9) + (4x)² - (2)²
B = (4x + 2)(7x - 9) + (4x - 2)(4x + 2)
B = (4x + 2)(7x - 9 + 4x - 2)
B = (4x + 2)(11x - 11)
B = 11(x - 1) * 2(2x + 1)
B = (11 * 2)(x - 1)(2x + 1)
B = 22(x - 1)(2x + 1)
Voilà