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P age 1/ 4 Développements - Classe de 3 e Corrigé de l’exercice 1 Dév elopp er

P age 1/ 4 Développements - Classe de 3 e Corrigé de l’exercice 1 Dév elopp er et réduire les expressions suiv an tes. A = (4 x + 3)2 A = (4 x)2 + 2 × 4 x × 3 + 32 A = 16 x2 + 24 x + 9 B = (4 x + 8) (4 x −8) B = (4 x)2 −82 B = 16 x2 −64 C = (6 x −3)2 C = (6 x)2 −2 × 6 x × 3 + 32 C = 36 x2 −36 x + 9 D = (−3 x + 3) (−5 x −10) D = 15 x2 + 30 x + (−15 x) + (−30) D = 15 x2 + 15 x −30 E = (−3 x −1) (−9 x −4) −(10 x + 10)2 E = 27 x2 + 12 x + 9 x + 4 −((10 x)2 + 2 × 10 x × 10 + 102) E = 27 x2 + 21 x + 4 −(100 x2 + 200 x + 100) E = 27 x2 + 21 x + 4 −100 x2 −200 x −100 E = −73 x2 −179 x −96 F = (5 x −6) (5 x + 6) + (10 x −1)2 F = (5 x)2 −62 + (10 x)2 −2 × 10 x × 1 + 12 F = 25 x2 −36 + 100 x2 −20 x + 1 F = 125 x2 −20 x −35 Corrigé de l’exercice 2 Dév elopp er et réduire les expressions suiv an tes. A = (−6 x + 2) (8 x −3) A = −48 x2 + 18 x + 16 x + (−6) A = −48 x2 + 34 x −6 B = (6 x + 8)2 B = (6 x)2 + 2 × 6 x × 8 + 82 B = 36 x2 + 96 x + 64 C = (6 x + 9) (6 x −9) C = (6 x)2 −92 C = 36 x2 −81 D = (5 x −1)2 D = (5 x)2 −2 × 5 x × 1 + 12 D = 25 x2 −10 x + 1 E = −(8 x + 9) (6 x + 3) −(6 x −10) (6 x + 10) E = −(48 x2 + 24 x + 54 x + 27) −((6 x)2 −102) Année 2013/2014 P age 2/ 4 Développements - Classe de 3 e E = −(48 x2 + 78 x + 27) −(36 x2 −100) E = −48 x2 −78 x −27 −36 x2 + 100 E = −84 x2 −78 x + 73 F = −(10 x −3)2 + (8 x + 10)2 F = −((10 x)2 −2 × 10 x × 3 + 32) + (8 x)2 + 2 × 8 x × 10 + 102 F = −(100 x2 −60 x + 9) + 64 x2 + 160 x + 100 F = −100 x2 + 60 x −9 + 64 x2 + 160 x + 100 F = −36 x2 + 220 x + 91 Corrigé de l’exercice 3 Dév elopp er et réduire les expressions suiv an tes. A = (6 x + 9)2 A = (6 x)2 + 2 × 6 x × 9 + 92 A = 36 x2 + 108 x + 81 B = (−5 x + 1) (7 x + 4) B = −35 x2 + (−20 x) + 7 x + 4 B = −35 x2 −13 x + 4 C = (8 x + 6) (8 x −6) C = (8 x)2 −62 C = 64 x2 −36 D = (5 x −9)2 D = (5 x)2 −2 × 5 x × 9 + 92 D = 25 x2 −90 x + 81 E = (3 x + 3) (3 x −3) + (7 x −9) (4 x + 6) E = (3 x)2 −32 + 28 x2 + 42 x + (−36 x) + (−54) E = 9 x2 −9 + 28 x2 + 6 x −54 E = 37 x2 + 6 x −63 F = (3 x −3)2 + (x + 10)2 F = (3 x)2 −2 × 3 x × 3 + 32 + x2 + 2 × x × 10 + 102 F = 9 x2 −18 x + 9 + x2 + 20 x + 100 F = 10 x2 + 2 x + 109 Corrigé de l’exercice 4 Dév elopp er et réduire les expressions suiv an tes. Année 2013/2014 P age 3/ 4 Développements - Classe de 3 e A = (−7 x −10) (−3 x + 5) A = 21 x2 + (−35 x) + 30 x + (−50) A = 21 x2 −5 x −50 B = (3 x −6) (3 x + 6) B = (3 x)2 −62 B = 9 x2 −36 C = (10 x −3)2 C = (10 x)2 −2 × 10 x × 3 + 32 C = 100 x2 −60 x + 9 D = (6 x + 9)2 D = (6 x)2 + 2 × 6 x × 9 + 92 D = 36 x2 + 108 x + 81 E = −(9 x + 2)2 −(8 x + 5) (8 x −5) E = −((9 x)2 + 2 × 9 x × 2 + 22) −((8 x)2 −52) E = −(81 x2 + 36 x + 4) −(64 x2 −25) E = −81 x2 −36 x −4 −64 x2 + 25 E = −145 x2 −36 x + 21 F = −(7 x + 7) (−7 x + 5) −(7 x −9)2 F = −(−49 x2 + 35 x + (−49 x) + 35) −((7 x)2 −2 × 7 x × 9 + 92) F = −(−49 x2 −14 x + 35) −(49 x2 −126 x + 81) F = 49 x2 + 14 x −35 −49 x2 + 126 x −81 F = 140 x −116 Corrigé de l’exercice 5 Dév elopp er et réduire les expressions suiv an tes. A = (7 x + 8) (7 x −8) A = (7 x)2 −82 A = 49 x2 −64 B = (3 x + 2)2 B = (3 x)2 + 2 × 3 x × 2 + 22 B = 9 x2 + 12 x + 4 C = (−5 x −1) (−10 x + 7) C = 50 x2 + (−35 x) + 10 x + (−7) C = 50 x2 −25 x −7 D = (5 x −1)2 D = (5 x)2 −2 × 5 x × 1 + 12 D = 25 x2 −10 x + 1 E = (3 x −3)2 −(−7 x −9) (−8 x −6) E = (3 x)2 −2 × 3 x × 3 + 32 −(56 x2 + 42 x + 72 x + 54) E = 9 x2 −18 x + 9 −(56 x2 + 114 x + 54) Année 2013/2014 P age 4/ 4 Développements - Classe de 3 e E = 9 x2 −18 x + 9 −56 x2 −114 x −54 E = −47 x2 −132 x −45 F = −(6 x −9) (6 x + 9) −(7 x + 2)2 F = −((6 x)2 −92) −((7 x)2 + 2 × 7 x × 2 + 22) F = −(36 x2 −81) −(49 x2 + 28 x + 4) F = −36 x2 + 81 −49 x2 −28 x −4 F = −85 x2 −28 x + 77 Corrigé de l’exercice 6 Dév elopp er et réduire les expressions suiv an tes. A = (7 x + 9)2 A = (7 x)2 + 2 × 7 x × 9 + 92 A = 49 x2 + 126 x + 81 B = (7 x −6)2 B = (7 x)2 −2 × 7 x × 6 + 62 B = 49 x2 −84 x + 36 C = (−10 x + 10) (5 x + 1) C = −50 x2 + (−10 x) + 50 x + 10 C = −50 x2 + 40 x + 10 D = (4 x + 8) (4 x −8) D = (4 x)2 −82 D = 16 x2 −64 E = (−4 x −4) (−5 x −10) + (7 x + 8) (7 x −8) E = 20 x2 + 40 x + 20 x + 40 + (7 x)2 −82 E = 20 x2 + 60 x + 40 + 49 x2 −64 E = 69 x2 + 60 x −24 F = (2 x + 7)2 + (8 x −10)2 F = (2 x)2 + 2 × 2 x × 7 + 72 + (8 x)2 −2 × 8 x × 10 + 102 F = 4 x2 + 28 x + 49 + 64 x2 −160 x + 100 F = 68 x2 −132 x + 149 Année 2013/2014 uploads/s3/ developpement-corrige-serie-d-exercices-1.pdf