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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 = (2 x + 9)2 A = (2 x)2 + 2 × 2 x × 9 + 92 A = 4 x2 + 36 x + 81 B = (x + 7) (−2 x + 8) B = −2 x2 + 8 x + (−14 x) + 56 B = −2 x2 −6 x + 56 C = (2 x −10)2 C = (2 x)2 −2 × 2 x × 10 + 102 C = 4 x2 −40 x + 100 D = (10 x −8) (10 x + 8) D = (10 x)2 −82 D = 100 x2 −64 E = (3 x −4)2 + (x −2) (−x + 3) E = (3 x)2 −2 × 3 x × 4 + 42 + −x2 + 3 x + 2 x + (−6) E = 9 x2 −24 x + 16 −x2 + 5 x −6 E = 8 x2 −19 x + 10 F = (7 x −8) (7 x + 8) + (6 x + 4)2 F = (7 x)2 −82 + (6 x)2 + 2 × 6 x × 4 + 42 F = 49 x2 −64 + 36 x2 + 48 x + 16 F = 85 x2 + 48 x −48 Corrigé de l’exercice 2 Dév elopp er et réduire les expressions suiv an tes. A = (9 x −5) (9 x + 5) A = (9 x)2 −52 A = 81 x2 −25 B = (5 x −9)2 B = (5 x)2 −2 × 5 x × 9 + 92 B = 25 x2 −90 x + 81 C = (10 x + 3)2 C = (10 x)2 + 2 × 10 x × 3 + 32 C = 100 x2 + 60 x + 9 D = (3 x + 8) (6 x −8) D = 18 x2 + (−24 x) + 48 x + (−64) D = 18 x2 + 24 x −64 E = (5 x −6) (5 x + 6) −(4 x −8) (7 x −8) E = (5 x)2 −62 −(28 x2 + (−32 x) + (−56 x) + 64) E = 25 x2 −36 −(28 x2 −88 x + 64) Année 2013/2014 P age 2/ 4 Développements - Classe de 3 e E = 25 x2 −36 −28 x2 + 88 x −64 E = −3 x2 + 88 x −100 F = (10 x −5)2 −(7 x + 7)2 F = (10 x)2 −2 × 10 x × 5 + 52 −((7 x)2 + 2 × 7 x × 7 + 72) F = 100 x2 −100 x + 25 −(49 x2 + 98 x + 49) F = 100 x2 −100 x + 25 −49 x2 −98 x −49 F = 51 x2 −198 x −24 Corrigé de l’exercice 3 Dév elopp er et réduire les expressions suiv an tes. A = (x −7) (−2 x −1) A = −2 x2 + (−x) + 14 x + 7 A = −2 x2 + 13 x + 7 B = (9 x + 2)2 B = (9 x)2 + 2 × 9 x × 2 + 22 B = 81 x2 + 36 x + 4 C = (6 x −5) (6 x + 5) C = (6 x)2 −52 C = 36 x2 −25 D = (5 x −7)2 D = (5 x)2 −2 × 5 x × 7 + 72 D = 25 x2 −70 x + 49 E = (4 x −8)2 + (−4 x −10) (−3 x −9) E = (4 x)2 −2 × 4 x × 8 + 82 + 12 x2 + 36 x + 30 x + 90 E = 16 x2 −64 x + 64 + 12 x2 + 66 x + 90 E = 28 x2 + 2 x + 154 F = (7 x + 3)2 + (5 x + 9) (5 x −9) F = (7 x)2 + 2 × 7 x × 3 + 32 + (5 x)2 −92 F = 49 x2 + 42 x + 9 + 25 x2 −81 F = 74 x2 + 42 x −72 Corrigé de l’exercice 4 Dév elopp er et réduire les expressions suiv an tes. A = (2 x + 9) (x + 4) A = 2 x2 + 8 x + 9 x + 36 A = 2 x2 + 17 x + 36 Année 2013/2014 P age 3/ 4 Développements - Classe de 3 e B = (5 x + 3) (5 x −3) B = (5 x)2 −32 B = 25 x2 −9 C = (7 x −1)2 C = (7 x)2 −2 × 7 x × 1 + 12 C = 49 x2 −14 x + 1 D = (7 x + 5)2 D = (7 x)2 + 2 × 7 x × 5 + 52 D = 49 x2 + 70 x + 25 E = (7 x + 9)2 + (5 x −10)2 E = (7 x)2 + 2 × 7 x × 9 + 92 + (5 x)2 −2 × 5 x × 10 + 102 E = 49 x2 + 126 x + 81 + 25 x2 −100 x + 100 E = 74 x2 + 26 x + 181 F = (8 x −7) (8 x + 7) + (x + 4) (−5 x + 5) F = (8 x)2 −72 + −5 x2 + 5 x + (−20 x) + 20 F = 64 x2 −49 −5 x2 −15 x + 20 F = 59 x2 −15 x −29 Corrigé de l’exercice 5 Dév elopp er et réduire les expressions suiv an tes. A = (8 x + 8) (8 x −8) A = (8 x)2 −82 A = 64 x2 −64 B = (5 x −6)2 B = (5 x)2 −2 × 5 x × 6 + 62 B = 25 x2 −60 x + 36 C = (3 x + 9)2 C = (3 x)2 + 2 × 3 x × 9 + 92 C = 9 x2 + 54 x + 81 D = (x + 10) (9 x −10) D = 9 x2 + (−10 x) + 90 x + (−100) D = 9 x2 + 80 x −100 E = −(9 x −4)2 + (3 x + 4)2 E = −((9 x)2 −2 × 9 x × 4 + 42) + (3 x)2 + 2 × 3 x × 4 + 42 E = −(81 x2 −72 x + 16) + 9 x2 + 24 x + 16 E = −81 x2 + 72 x −16 + 9 x2 + 24 x + 16 Année 2013/2014 P age 4/ 4 Développements - Classe de 3 e E = −72 x2 + 96 x F = (x + 7) (−2 x −5) + (6 x −2) (6 x + 2) F = −2 x2 + (−5 x) + (−14 x) + (−35) + (6 x)2 −22 F = −2 x2 −19 x −35 + 36 x2 −4 F = 34 x2 −19 x −39 Corrigé de l’exercice 6 Dév elopp er et réduire les expressions suiv an tes. A = (10 x −7) (10 x + 7) A = (10 x)2 −72 A = 100 x2 −49 B = (6 x −8)2 B = (6 x)2 −2 × 6 x × 8 + 82 B = 36 x2 −96 x + 64 C = (x + 6)2 C = x2 + 2 × x × 6 + 62 C = x2 + 12 x + 36 D = (−10 x + 5) (−7 x −9) D = 70 x2 + 90 x + (−35 x) + (−45) D = 70 x2 + 55 x −45 E = −(−7 x + 9) (6 x −3) −(5 x + 10)2 E = −(−42 x2 + 21 x + 54 x + (−27)) −((5 x)2 + 2 × 5 x × 10 + 102) E = −(−42 x2 + 75 x −27) −(25 x2 + 100 x + 100) E = 42 x2 −75 x + 27 −25 x2 −100 x −100 E = 17 x2 −175 x −73 F = −(3 x + 10) (3 x −10) + (2 x −9)2 F = −((3 x)2 −102) + (2 x)2 −2 × 2 x × 9 + 92 F = −(9 x2 −100) + 4 x2 −36 x + 81 F = −9 x2 + 100 + 4 x2 −36 x + 81 F = −5 x2 −36 x + 181 Année 2013/2014 uploads/s3/ developpement-corrige-serie-d-exercices-2 1 .pdf