Les 3 identités remarquables

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1 Les 3 identités remarquables
(x + …)² = x² + 6x + … … – … + 4 = (2x – …)² (3 – …)(3 + …) = … – x²

2 Calcul 1 36a² – 12a + 1 = (…a .. …)²

3 Calcul 2 (… – …)(… + 8) = 16x²– …

4 Calcul 3 (…x .. 1)² = 81x ² – 18x +…

5 Calcul 4 (2x + …)(… – …) = …x² – 49

6 Calcul 5 25x² + …x + 1 = (…x + …)²

7 Prêt pour la correction…

8 Calcul 1 36a² – 12a + 1 = (…a .. …)²

9 a = 6a et b = 1 a² – 2ab + b² = (a – b)² 36a² – 12a + 1 = (…a .. …)²
Calcul 1 a² – 2ab + b² = (a – b)² 36a² – 12a + 1 = (…a .. …)² a = 6a et b = 1

10 a = 6a et b = 1 a² – 2ab + b² = (a – b)²
Calcul 1 a² – 2ab + b² = (a – b)² (6a)² – 2 x 6a x 1 + 1² = (…a .. …)² a = 6a et b = 1

11 a = 6a et b = 1 a² – 2ab + b² = (a – b)²
Calcul 1 a² – 2ab + b² = (a – b)² (6a)² – 2 x 6a x 1 + 1² = (…a .. …)² a = 6a et b = 1

12 a = 6a et b = 1 a² – 2ab + b² = (a – b)² 36a² – 12a + 1 = (6a – 1)²
Calcul 1 a² – 2ab + b² = (a – b)² 36a² – 12a + 1 = (6a – 1)² a = 6a et b = 1

13 Calcul 2 (… – …)(… + 8) = 16x²– …

14 (a – b)(a + b) = a² – b² (… – …)(… + 8) = 16x²– … a = 4x et b = 8
Calcul 2 (a – b)(a + b) = a² – b² (… – …)(… + 8) = 16x²– … a = 4x et b = 8

15 (a – b)(a + b) = a² – b² a = 4x et b = 8 (… – …)(… + 8) = (4x)²– …
Calcul 2 (a – b)(a + b) = a² – b² (… – …)(… + 8) = (4x)²– … a = 4x et b = 8

16 (a – b)(a + b) = a² – b² a = 4x et b = 8 (… – …)(… + 8) = (4x)²– …
Calcul 2 (a – b)(a + b) = a² – b² (… – …)(… + 8) = (4x)²– … a = 4x et b = 8

17 (a – b)(a + b) = a² – b² a = 4x et b = 8 (4x – 8)(4x + 8) = 16x²– 64
Calcul 2 (a – b)(a + b) = a² – b² (4x – 8)(4x + 8) = 16x²– 64 a = 4x et b = 8

18 Calcul 3 (…x .. 1)² = 81x ² – 18x +…

19 (a – b)² = a² – 2ab + b² a = 9x et b = 1 (…x .. 1)² = 81x ² – 18x +…
Calcul 3 (a – b)² = a² – 2ab + b² (…x .. 1)² = 81x ² – 18x +… a = 9x et b = 1

20 (a – b)² = a² – 2ab + b² a = 9x et b = 1
Calcul 3 (a – b)² = a² – 2ab + b² (…x .. 1)² = (9x)² – 2 x 9x x 1+… a = 9x et b = 1

21 (a – b)² = a² – 2ab + b² a = 9x et b = 1
Calcul 3 (a – b)² = a² – 2ab + b² (…x .. 1)² = (9x)² – 2 x 9x x 1+… a = 9x et b = 1

22 (a – b)² = a² – 2ab + b² a = 9x et b = 1 (9x – 1)² = 81x ² – 18x + 1
Calcul 3 (a – b)² = a² – 2ab + b² (9x – 1)² = 81x ² – 18x + 1 a = 9x et b = 1

23 Calcul 4 (2x + …)(… – …) = …x² – 49

24 (a + b)(a – b) = a² – b² a = 2x et b = 7 (2x + …)(… – …) = …x² – 49
Calcul 4 (a + b)(a – b) = a² – b² (2x + …)(… – …) = …x² – 49 a = 2x et b = 7

25 (a + b)(a – b) = a² – b² a = 2x et b = 7 (2x + …)(… – …) = …x² – 7²
Calcul 4 (a + b)(a – b) = a² – b² (2x + …)(… – …) = …x² – 7² a = 2x et b = 7

26 (a + b)(a – b) = a² – b² a = 2x et b = 7 (2x + …)(… – …) = …x² – 7²
Calcul 4 (a + b)(a – b) = a² – b² (2x + …)(… – …) = …x² – 7² a = 2x et b = 7

27 (a + b)(a – b) = a² – b² a = 2x et b = 7 (2x + 7)(2x – 7) = 4x² – 49
Calcul 4 (a + b)(a – b) = a² – b² (2x + 7)(2x – 7) = 4x² – 49 a = 2x et b = 7

28 Calcul 5 25x² + …x + 1 = (…x + …)²

29 a = 5x et b = 1 a² + 2ab + b² = (a + b)² 25x² + …x + 1 = (…x + …)²
Calcul 5 a² + 2ab + b² = (a + b)² 25x² + …x + 1 = (…x + …)² a = 5x et b = 1

30 a = 5x et b = 1 a² + 2ab + b² = (a + b)² (5x)² + …x + 1² = (…x + …)²
Calcul 5 a² + 2ab + b² = (a + b)² (5x)² + …x + 1² = (…x + …)² a = 5x et b = 1

31 a = 5x et b = 1 a² + 2ab + b² = (a + b)² (5x)² + …x + 1² = (…x + …)²
Calcul 5 a² + 2ab + b² = (a + b)² (5x)² + …x + 1² = (…x + …)² a = 5x et b = 1

32 a = 5x et b = 1 a² + 2ab + b² = (a + b)² 25x² + 10x + 1 = (5x + 1)²
Calcul 5 a² + 2ab + b² = (a + b)² 25x² + 10x + 1 = (5x + 1)² a = 5x et b = 1

33 1. 36a² – 12a + 1 = (6a – 1)² 2. (4x – 8)(4x + 8) = 16x²– 64 3. (9x – 1)² = 81x ² – 18x + 1 4. (2x + 7)(2x – 7) = 4x² – 49 5. 25x² + 10x + 1 = (5x + 1)²