Sagot :
Bonsoir,
1) Développer : 3(2x - 1)² + 2(2x - 1)
3(2x - 1)² + 2(2x - 1) = 3(4x² - 4x + 1) + 4x - 2
= 12x² - 12x + 3 + 4x - 2
= 12x² - 8x + 1
Factoriser : 3(2x-1)² + 2(2x-1)
3(2x - 1)² + 2(2x - 1) = 3(2x - 1)(2x - 1) + 2(2x - 1)
= (2x - 1)[(3(2x - 1) + 2]
= (2x - 1)(6x - 3 + 2)
= (2x - 1)(6x - 1)
2) donner le résultat sous forme d'un seul quotient :
(2/5-3/7) (2/11)
(1/3-2) (4/5_1)
[tex]\dfrac{(\dfrac{2}{5}-\dfrac{3}{7})\times \dfrac{2}{11}}{(\dfrac{1}{3}-2)(\dfrac{4}{5}-1)}=\dfrac{(\dfrac{14}{35}-\dfrac{15}{35})\times \dfrac{2}{11}}{(\dfrac{1}{3}-\dfrac{6}{3})(\dfrac{4}{5}-\dfrac{5}{5})}=\dfrac{(-\dfrac{1}{35})\times \dfrac{2}{11}}{(-\dfrac{5}{3})(-\dfrac{1}{5})}\\\\\\=\dfrac{-\dfrac{2}{385}}{\dfrac{1}{3}}=(-\dfrac{2}{385})\times\dfrac{3}{1}=-\dfrac{6}{385}[/tex]
1) Développer : 3(2x - 1)² + 2(2x - 1)
3(2x - 1)² + 2(2x - 1) = 3(4x² - 4x + 1) + 4x - 2
= 12x² - 12x + 3 + 4x - 2
= 12x² - 8x + 1
Factoriser : 3(2x-1)² + 2(2x-1)
3(2x - 1)² + 2(2x - 1) = 3(2x - 1)(2x - 1) + 2(2x - 1)
= (2x - 1)[(3(2x - 1) + 2]
= (2x - 1)(6x - 3 + 2)
= (2x - 1)(6x - 1)
2) donner le résultat sous forme d'un seul quotient :
(2/5-3/7) (2/11)
(1/3-2) (4/5_1)
[tex]\dfrac{(\dfrac{2}{5}-\dfrac{3}{7})\times \dfrac{2}{11}}{(\dfrac{1}{3}-2)(\dfrac{4}{5}-1)}=\dfrac{(\dfrac{14}{35}-\dfrac{15}{35})\times \dfrac{2}{11}}{(\dfrac{1}{3}-\dfrac{6}{3})(\dfrac{4}{5}-\dfrac{5}{5})}=\dfrac{(-\dfrac{1}{35})\times \dfrac{2}{11}}{(-\dfrac{5}{3})(-\dfrac{1}{5})}\\\\\\=\dfrac{-\dfrac{2}{385}}{\dfrac{1}{3}}=(-\dfrac{2}{385})\times\dfrac{3}{1}=-\dfrac{6}{385}[/tex]
