déveloper et réduire l'expression A = (2x + 1) (1 + 2x) - 10x carré + 9x + 7 Démontrer que A = 3 (1 + 2x) (2 - x) Calculer les valeurs prise par A pour: x = 1/2

Question 1.

A = (2x-1)(1+2x) - 10x² + 9x + 7
A = 2x*1 + 2x*2x + (-1)*1 + (-1)*2x - 10x² + 9x + 7
A = 2x + 4x² - 1 - 2x - 10x² + 9x + 7
A = 4x² - 10x² + 2x - 2x + 9x - 1 + 7
A = - 6x² + 9x + 6

Question 2.

B = 3(1+2x)(2-x)
B = 3(1*2 + 1*(-x) + 2x*2 + 2x*(-x)
B = 3(2 - x + 4x - 2x²)
B = 3(-2x² + 3x + 2)
B = - 6x² + 9x + 6
B = A

Question 3.

Si x=1/2.

A = 3(1+2*1/2)(2-1/2)
A = 3(1+1)(4/2-1/2)
A = 3*2*3/2
A = 9

Si x=1.

A = 3(1+1*2)(2-1)
A = 3(1+2)*1
A = 3*3
A = 9

Si x=0.

A = 3(1+2*0)(2-0)
A = 3*1*2
A = 6