Développer les expressions suivantes en utilisant les identités remarquables : a. (x + 3)2 b. (x – 5)2 c. (4 + 5x)2 d. (3 – 2x)2 e. (1 + 4x)(1 - 4x) f. (8 + 3x)

Réponse:

Bonsoir l'ami ! :)

a = (x+3)^2

= x^2 + 2x x 3 + 3^2

= x^2 + 6x + 9

b = (x-5)^2

= x^2 - 2x x 5 + 5^2

= x^2 - 10x + 25

c = (4+5x)^2

= 4^2 + 2 x 4 x 5x + 5x^2

= 16 + 40x + 25x^2

= 25x^2 + 40x + 16

d = (3-2x)^2

= 3^2 - 2 x 3 x 2x + 2x^2

= 9 - 12x + 4x^2

= 4x^2 - 12x + 9

e = (1+4x)(1-4x)

= 1^2 - (4x)^2

= 1 - 16x^2

f = (8+3x)(-3x+8)

= (8+3x)(8-3x)

= 64 - 9x^2