Salut ! :)
Exercice 1
a) (3x + 1)² = (3x)² + 2×3x×1 + 1²
= 9x² + 6x + 1
b) (7 - x)² = 7² - 2×7×x + x²
= 49 - 14x + x²
= x² - 14x + 49
c) (9 - 5x)(9 + 5x) = 9² - (5x)²
= 81 - 25x²
Exercice 2
a) 36 - 60x + 25x² = 6² - 2×6×5x + (5x)²
= (6 - 5x)²
b) 9x² + 42x + 49 = (3x)² + 2×3x×7 + 7²
= (3x + 7)²
c) x² - 9/16 = x² - (3/4)²
= (x - 3/4)(x + 3/4)
d) 1 - 16y² = 1² - (4y)²
= (1 - 4y)(1 + 4y)
Exercice 3
a) K = (n + 1)² - (n - 1)²
= n² + 2n + 1 - (n² - 2n + 1)
= n² + 2n + 1 - n² + 2n - 1
= 4n
b) K = (n + 1)² - (n - 1)²
= (n+1 - (n - 1)) (n+1 + n -1)
= (n + 1 - n + 1)( 2n)
= 2×2n
= 4n
A retenir :
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a - b)(a + b) = a² - b²
Voilà, j'espère t'avoir aidé. :)
