Réponse :
Explications étape par étape
Bonjour’
Factoriser les expressions suivantes :
1) 10+45x+20y
= 5 * 2 + 5 * 9x + 5 * 4y
= 5(2 + 9x + 4y)
2) (5x−5)(5x+2)+7(5x−5)
= (5x - 5)(5x + 2 + 7)
= 5(x - 1)(5x + 9)
3) (−5x+3)(7x−4)+(−5x+3)(−9x+5)
= (-5x + 3)(7x - 4 - 9x + 5)
= (-5x + 3)(-2x + 1)
4) (9x−7)au carré +(9x−7)(−5x+6)
= (9x - 7)(9x - 7 - 5x + 6)
= (9x - 7)(4x - 1)
5) (−9x−6)(−4x+6)−(−9x−6)(6x+5)
= (-9x - 6)(-4x + 6 - 6x - 5)
= (-3)(3x + 2)(-10x + 1)
6) 49x au carré −98x+49
= 49 * x^2 - 49 * 2x + 49 * 1
= 49(x^2 - 2x + 1)
= 49(x - 1)^2
7) 4x au carré - 16
= (2x)^2 - 4^2
= (2x - 4)(2x + 4)
= 2(x - 2) * 2(x + 2)
= 4(x - 2)(x + 2)
8) 16x au carré −24x+9
= (4x)^2 - 2 * 4x * 3 + 3^2
= (4x - 3)^2
9) 4x au carré −49
= (2x)^2 - 7^2
= (2x - 7)(2x + 7)
10) 36x au carré +84x+49
= (6x)^2 + 2 * 6x * 7 + 7^2
= (6x + 7)^2