Réponse :
Explications étape par étape :
Exercice 25
A= (x+2)²-3(x+1)² = x²+4x+4 -3(x²+2x+1)
= x²+4x+4 -3x²-6x-3 = -2x² -2x +1
B= (x-3)²+2(x-1)² = x²-6x+9 +2(x²-2x+1)
= x²-6x+9 +2x²-4x+2 = 3x²-10x+11
C= -(2x-1)² +(x+3)² = -(4x²-4x+1) + x²+6x+9
= -4x²+4x-1+x²+6x+9= -3x²+10x+8
D= (2x-3)(2x+3) –(x+1)(x-1)= 4x²-9 – (x²-1)
=4x²-9-x²+1 = 3x²-8
E= 5(x+1/2)(1/2-x) – 2(3x+1)(-3x+1)
=-5(x+1/2)(x-1/2) +2 (3x+1)(3x-1)
= -5(x² - ¼) +2(9x²-1)
= -5x² +5/4 +18x² -2
= 13x² - 3/4
Exercice 26
A= 4(x/2 -1)(x/2 +1) –x(1-x)(x+1)
=4(x²/4-1) +x(x-1)(x+1) = x² -4 +x(x²-1)
=x²-4 + x³-x = x³+x²-x-4
B=(-3x-1)(1-3x) – (2x+1)²
= (-3x-1)(-3x+1) – (4x²+4x+1)
= 9x²-1 -4x²-4x-1
= 5x² -4x -2
C= (3t-5)(5+3t) – 2(2t-1)²
= (3t-5)(3t+5) -2(4t²-4t+1)
= 9t²-25 -8t²+8t -2
= t² +8t -27
D = 2(2-y)² + 3(2y+1)² - 2(3y-2)²
= 2(4-4y+y²) +3(4y²+4y+1) -2(9y²-12y+4)
= 8 -8y +2y² +12y² +12y +3 -18y² +24y -8
= -4y² + 28y + 3
