Réponse :
E = (- 1 + 2 x)² - (3 - 6 x)(1 - x)
a) E = (- 1 + 2 x)² - (3 - 6 x)(1 - x)
= 1 - 4 x + 4 x² - (3 - 9 x + 6 x²)
= 1 - 4 x + 4 x² - 3 + 9 x - 6 x²
= - 2 x² + 5 x - 2
b) E = - 2 x² + 5 x - 2
= - 2(x² - (5/2) x + 1)
= - 2(x² - (5/2) x + 1 + 25/16 - 25/16)
= - 2(x² - (5/2) x + 25/16 - 9/16)
= - 2((x - 5/4)² - (3/4)²) identité remarquable
= - 2(x - 5/4 + 3/4)(x - 5/4 - 3/4)
= - 2(x - 1/2)(x - 2)
= (2 x - 1)(- x + 2)
3) E = - 2((x - 5/4)² - 9/16) = - 2(x - 5/4)² + 9/8
Explications étape par étape :
