Bonjour, j'ai un dm à rendre et voila les exerices : Ex 1 : Développer et réduire : A: (4x−1)²+(x+2)² B: (5t+4)²+(5t+4)(5t−4) C: (7x−1)²+(7x+1)² D: (5a−4)(a+2)

Bonjour,

Ex 1 : Développer et réduire :

A: (4x−1)²+(x+2)²
= 16x² - 8x + 1 + x² + 4x + 4
= 16x² + x² - 8x + 4x + 1 + 4
= 17x² - 4x + 5

B: (5t+4)²+(5t+4)(5t−4)
= 25t² + 40t + 16 + 25t² - 20t + 20t - 16
= 25t² + 25t² + 40t + 20t - 20t + 16 - 16
= 40t

C: (7x−1)²+(7x+1)²
= 49x² - 28x + 1 + 49x² + 14x + 1
= 49x² + 49x² - 28x + 14x + 1 + 1
= 98x² - 14x + 2

D: (5a−4)(a+2)−(a+2)²
= 5a² + 10a - 4a - 8 - (a² + 4a + 4)
= 5a² + 10a - 4a - 8 - a² - 4a - 4
= 5a² - a² + 10a - 4a - 4a - 8 - 4
= 4a² + 2a - 12

E: −3(t−2)+5(t−1)²
= - 3t + 6 + 5 (t² - 2t + 1)
= - 3t + 6 + 5t² - 10t + 5
= 5t² - 3t - 10t + 6 + 5
= 5t² - 13t + 11

F: 4(1/2×−1)²−(x−4)(x+4)
= 4 (0,25x² - 0,5 + 1) - (x² + 4x - 4x - 16)
= x² - 2 + 4 - x² - 4x + 4x + 16
= x² - x² - 4x + 4x - 2 + 4 + 16
= 18

A = (4x - 1)² + (x + 2)²
A = [(4x)² - 2 X 4x X 1 + 1²] + [x² + 2 X x X 2 + 2²]
A = 16x² - 8x + 1 + x² + 4x + 4
A = 17x² - 4x + 5

B = (5t + 4)² + (5t + 4) (5t - 4)
B = [(5t)² + 2 X 5t X 4 + 4²] + (5t)² - 4²
B = 25t² + 40t + 16 + 25t² - 16
B = 50t² + 40t

C = (7x - 1)² + (7x + 1)²
C = [(7x)² - 2 X 7x X 1 + 1²] + [(7x)² + 2 X 7x X 1 + 1²]
C = 49x² - 14x + 1 + 49x² + 14x + 1
C = 98x² + 2

D = (5a - 4) (a + 2) - (a + 2)²
D = 5a X a + 5a X 2 - 4 X a - 4 X 2 - [a² + 2 X a X 2 + 2²]
D = 5a² + 10a - 4a - 8 - (a² + 4a + 4)
D = 5a² + 10a - 4a - 8 - a² - 4a - 4
D = 4a² + 2a - 12

E = - 3 (t - 2) + 5 (t - 1)²
E = - 3 X t - 3 X (- 2) + 5 X [t² - 2 X t X 1 + 1²]
E = - 3t + 6 + 5 X (t² - 2t + 1)
E = - 3t + 6 + 5 X t² + 5 X (- 2t) + 5 X 1
E = - 3t + 6 + 5t² - 10t + 5
E = - 5t² - 13t + 11

F = 4 (1/2 X - 1)² - (x - 4) (x + 4)
F = 4 (0,25x² - 0,5 + 1) - [x² - 4²]
F = x² - 2 + 4 - (x² - 16)
F = x² - 2 + 4 - x² + 16
F = 18