Page 1/ 3 identités remarquables - http://www.toupty.com Classe de 3e Corrigé d

Page 1/ 3 identités remarquables - http://www.toupty.com Classe de 3e Corrigé de l’exercice 1 Développer chacune des expressions littérales suivantes : A = (9 x −8)2 A = (9 x)2 −2 × 9 x × 8 + 82 A = 81 x2 −144 x + 64 B = (7 x −5) × (7 x + 5) B = (7 x)2 −52 B = 49 x2 −25 C = (5 x + 4)2 C = (5 x)2 + 2 × 5 x × 4 + 42 C = 25 x2 + 40 x + 16 D = (9 x + 1) × (x −9) D = 9 x × x + 9 x × (−9) + 1 × x + 1 × (−9) D = 9 x2 −81 x + x −9 D = 9 x2 + (−81 + 1) x −9 D = 9 x2 −80 x −9 E = −(10 x −9)2 E = −  (10 x)2 −2 × 10 x × 9 + 92 E = − 100 x2 −180 x + 81  E = −100 x2 + 180 x −81 F =  8 x + 2 7  ×  8 x −2 7  F = (8 x)2 − 2 7 2 F = 64 x2 −4 49 Corrigé de l’exercice 2 Développer chacune des expressions littérales suivantes : A = (2 x + 8)2 A = (2 x)2 + 2 × 2 x × 8 + 82 A = 4 x2 + 32 x + 64 B = (6 x −7) × (6 x + 7) B = (6 x)2 −72 B = 36 x2 −49 C = (3 x −3)2 C = (3 x)2 −2 × 3 x × 3 + 32 C = 9 x2 −18 x + 9 D = (7 x + 5) × (5 x −7) D = 7 x × 5 x + 7 x × (−7) + 5 × 5 x + 5 × (−7) D = 35 x2 −49 x + 25 x −35 D = 35 x2 + (−49 + 25) x −35 D = 35 x2 −24 x −35 E = −(x −2)2 E = − x2 −2 × x × 2 + 22 E = − x2 −4 x + 4  E = −x2 + 4 x −4 F =  1 10 x + 9 7 2 F =  1 10 x 2 + 2 × 1 10 x × 9 7 + 9 7 2 F = 1 100 x2 + 9 ×  2 35 ×  2 x + 81 49 F = 1 100 x2 + 9 35 x + 81 49 Corrigé de l’exercice 3 Développer chacune des expressions littérales suivantes : A = (5 x −8)2 A = (5 x)2 −2 × 5 x × 8 + 82 A = 25 x2 −80 x + 64 B = (5 x −8) × (5 x + 8) B = (5 x)2 −82 B = 25 x2 −64 Année 2014/2015 http://www.pyromaths.org Page 2/ 3 identités remarquables - http://www.toupty.com Classe de 3e C = (10 x + 1) × (x −10) C = 10 x × x + 10 x × (−10) + 1 × x + 1 × (−10) C = 10 x2 −100 x + x −10 C = 10 x2 + (−100 + 1) x −10 C = 10 x2 −99 x −10 D = (2 x + 8)2 D = (2 x)2 + 2 × 2 x × 8 + 82 D = 4 x2 + 32 x + 64 E = −(10 x −7) × (10 x + 7) E = −  (10 x)2 −72 E = − 100 x2 −49  E = −100 x2 + 49 F = 4 3 x −7 3  × 7 3 x + 4 3  F = 4 3 x × 7 3 x + 4 3 x × 4 3 −7 3 × 7 3 x −7 3 × 4 3 F = 28 9 x2 + 16 9 x −49 9 x −28 9 F = 28 9 x2 + 16 9 −49 9  x −28 9 F = 28 9 x2 −33 9 x −28 9 F = 28 9 x2 −11 ×  3  3 × 3 x −28 9 F = 28 9 x2 −11 3 x −28 9 Corrigé de l’exercice 4 Développer chacune des expressions littérales suivantes : A = (x + 5)2 A = x2 + 2 × x × 5 + 52 A = x2 + 10 x + 25 B = (7 x + 7) × (7 x −7) B = (7 x)2 −72 B = 49 x2 −49 C = (2 x −1) × (2 x + 1) C = (2 x)2 −12 C = 4 x2 −1 D = (9 x −8)2 D = (9 x)2 −2 × 9 x × 8 + 82 D = 81 x2 −144 x + 64 E = −(x + 5) × (x −5) E = − x2 −52 E = − x2 −25  E = −x2 + 25 F =  3 10 x −5 8  × 5 8 x + 3 10  F = 3 10 x × 5 8 x + 3 10 x × 3 10 −5 8 × 5 8 x −5 8 × 3 10 F = 3 ×  5 16 ×  5 x2 + 9 100 x −25 64 x −3 ×  5 16 ×  5 F = 3 ×  5 16 ×  5 x2 +  9 100 −25 64  x −3 ×  5 16 ×  5 F = 3 16 x2 +  9×16 100×16 −25×25 64×25  x −3 16 F = 3 16 x2 +  144 1600 −625 1600  x −3 16 F = 3 16 x2 −481 1600 x −3 16 Corrigé de l’exercice 5 Développer chacune des expressions littérales suivantes : A = (10 x + 8) × (10 x −8) A = (10 x)2 −82 A = 100 x2 −64 B = (6 x + 6)2 B = (6 x)2 + 2 × 6 x × 6 + 62 B = 36 x2 + 72 x + 36 C = (3 x −4)2 C = (3 x)2 −2 × 3 x × 4 + 42 C = 9 x2 −24 x + 16 Année 2014/2015 http://www.pyromaths.org Page 3/ 3 identités remarquables - http://www.toupty.com Classe de 3e D = (7 x −9) × (9 x + 7) D = 7 x × 9 x + 7 x × 7 −9 × 9 x −9 × 7 D = 63 x2 + 49 x −81 x −63 D = 63 x2 + (49 −81) x −63 D = 63 x2 −32 x −63 E = −(8 x + 1) × (x −8) E = −(8 x × x + 8 x × (−8) + 1 × x + 1 × (−8)) E = − 8 x2 −64 x + x −8  E = − 8 x2 + (−64 + 1) x −8  E = − 8 x2 −63 x −8  E = −8 x2 + 63 x + 8 F = 7 2 x −8 7 2 F = 7 2 x 2 + 2 × 7 2 x × 8 7 + 8 7 2 F = 49 4 x2 + 8 ×  14 1 ×  14 x + 64 49 F = 49 4 x2 + 8 x + 64 49 Corrigé de l’exercice 6 Développer chacune des expressions littérales suivantes : A = (9 x + 3)2 A = (9 x)2 + 2 × 9 x × 3 + 32 A = 81 x2 + 54 x + 9 B = (4 x −8) × (8 x + 4) B = 4 x × 8 x + 4 x × 4 −8 × 8 x −8 × 4 B = 32 x2 + 16 x −64 x −32 B = 32 x2 + (16 −64) x −32 B = 32 x2 −48 x −32 C = (10 x + 8) × (10 x −8) C = (10 x)2 −82 C = 100 x2 −64 D = (9 x −10)2 D = (9 x)2 −2 × 9 x × 10 + 102 D = 81 x2 −180 x + 100 E = −(2 x + 4)2 E = −  (2 x)2 + 2 × 2 x × 4 + 42 E = − 4 x2 + 16 x + 16  E = −4 x2 −16 x −16 F = 1 9 x −7 6 2 F = 1 9 x 2 −2 × 1 9 x × 7 6 + 7 6 2 F = 1 81 x2 −7 ×  2 27 ×  2 x + 49 36 F = 1 81 x2 uploads/s3/ identite-remarquable-1-corrige 2 .pdf

Tags
Administrationcorrigé l’exercice développer chacune expressions
Documents similaires
  • 13
  • 0
  • 0
Afficher les détails des licences
Licence et utilisation
Gratuit pour un usage personnel Attribution requise
Partager