Réponse :
Explications étape par étape
■ exo 1 :
A = (x-5)² + (x-5)(x+1)
= (x-5) [ x-5 + x+1 ]
= (x-5) (2x-4)
= 2x² - 4x - 10x + 20 .
B = (2t/3 + 1/5)² = 4t²/9 + 4t/15 + 1/25 .
C = (4y+7)(4y-7) - (y+1)(y-1)
= 16y²-49 - [ y²-1 ]
= 15y² - 48 .
D = x(2x-5)² = x [ 4x² - 20x + 25 ]
= 4x³ - 20x² + 25x .
■ exo 2 :
E = A = 2(x-5)(x-2) .
F = (2x-1)(x+2) - (2x-1)²
= (2x-1) [ x+2 - 2x + 1 ] = (2x-1)(3-x) .
H = (x-1)² - 25 = (x-1-5)(x-1+5)
= (x-6)(x+4) .
I = (x-2)² - (3x-5)²
= (x-2 - 3x + 5)(x-2 + 3x-5)
= (3-2x)(4x-7) .
■ exo 3 :
A(0) = A(-1/3) = 0 .
A(t) = (3t+1) [ 3t+1 + t-1 ] = (3t+1)(4t)
= 4t(3t+1) --> forme factorisée .
A(t) = 12t² + 4t --> forme développée .
A(t) = 12 (t + 1/6)² - 1/3
= 12(t² + t/3 + 1/36) - 1/3
= 12t² + 4t + 1/3 - 1/3
= 12t² + 4t --> vérifié !
■ exo 4 :
Aire carré = 4² = 16 cm² .
Aire triangle ABM = 4x/2 = 2x .
Aire trapèze AMCD = 16 - 2x .
Aire AMCD = 14 cm² pour x = 1 cm .
Aire AMCD = 11 cm² pour x = 2,5 cm .
il faut bien entendu 0 < x ≤ 4 cm .
