Exercice 1
A = (x+4)² = x²+2*x*4+4² = x²+8x+16
B = (2-x)² = 2²-2*2*x+x² = 4-4x+x² = x²-4x+4
C = (x+1) (x-1) = x²-1² = x²-1
D = (2x+1)² = (2x)²+2*2x*1+1² = 4x²+4x+1
E = (3-2x)² = 3²-2*3*2x+(2x)² = 9-12x+4x² = 4x²-12x+9
F = (7x+5)² = (7x)²+2*7x*5+5² = 49x²+70x+25
G = (5x+6) (5x-6) = (5x)²-6² = 25x²-36
H = (4-8x)² = 4²-2*4*8x+(8x)² = 16-64x+64x² = 64x²-64x+16
I = (3+4x) (3-4x) = 3²-(4x)² = 9-16x² = 16x²-9
J = (3+x) (x-3) = (x+3) (x-3) = x²-3² = x²-9
K = (2+9x)² = 2²+2*2*9x+(9x)² = 4+36x+81x² = 81x²+36x+4
L = (11x-12)² = (11x)²-2*11x*12+12² = 121x²-264x+144
Exercice 2
A = (x+1)²+(x-3)² = x²+2*x*1+1²+x²-2*x*3 = x²+2x+1-x²-6x+9 = -4x+10
B = (3-x)² + (x+5)² = 3²-2*3*x+x²+x²+2*x*5+5² = 9-6x+x²+x²+10x+25 = x^4+4x+34
C = (x-2)²+(x+4) (x-4) = x²-2*x*2+2²+x²-4 = x²-4x+4+x²-16 = x^4-4x-12
D = (x+1) (x-1) + (x+4)² = x²-1²+x²+2*x*4+4² = x²-1+x²+8x+16 = x^4+8x+15
E = (x-5)² + (2x+7) (2x-7) = x²-2*x*5+5²+(2x)²-7² = x²-10x+25+4x²+49 = 5x²-10x-24
Exercice 3
A = (2x+1)²-(x+3)² = (2x)²+2*2x*1+1²-x²+2*x*3+3² = 4x²+4x+1-x²+6x+9 = 3x²+10x+10
B = (2x+3)² - (x-7) (x+7) = (2x)² +2*2x*3+3²-x²-7² = 4x²+12x+9-x²-49 = 3x²+12x-40
C = (x+2) (x-2) - (x-3)² = x²-2²-x²-2*x*3+3² = x²-4-x²-6x+9 = -6x+5
D = (x-5)² - (2x-7) (x-5) = x²-2*x*5+5²-(2x)²-10x-7x+35 = x²-10x+25-4x²-10x-7x+35 = 3x²-27x+60
E = (3x+1) (x-2) - (2x-3)² = 3x²-6x+x-2-(2x)²-2*2x*3+3² = 3x²-6x+x-2 -4x²-12x+9 = -x²-17x+7
