Bonjour,
Developper :
(x - 3)(x^2 + 4x - 5)
= x * x^2 + x * 4x - x * 5 - 3 * x^2 - 3 * 4x + 3 * 5
= x^3 + 4x^2 - 5x - 3x^2 - 12x + 15
= x^3 + x - 17x + 15
5x(x + 2)(x - 7)
= 5x(x * x - x * 7 + 2 * x - 2 * 7)
= 5x(x^2 - 7x + 2x - 14)
= 5x * x^2 - 5x * 7x + 5x * 2x - 5x * 14
= 5x^3 - 35x^2 + 10x^2 - 70x
= 5x^3 - 25x^2 - 70x
identité remarquable :
(a - b)^2 = a^2 - 2ab + b^2
3(x - 5)^2 - 10
= 3(x^2 - 10x + 25) - 10
= 3x^2 - 30x + 75 - 10
= 3x^2 - 30x + 65
(2x - 5)^2 - (3x - 1)(x - 2)
= 4x^2 - 20x + 25 - (3x^2 - 6x - x + 2)
= 4x^2 - 20x + 25 - 3x^2 + 6x + x - 2
= x^2 - 14x + 23
