1) a=1 et b=5
A = 1/4 ((1+5)²-(1-5)²) = 1/4 (6²-(-4)²) = 1/4 (36 - 16) = 1/4 (20) = 20/4 = 5
2) a=-2 et b=-3
A = 1/4 ((-2+(-3))²-(-2-(-3))²) = 1/4 ((-5)²- 1²) = 1/4 (25 - 1) = 1/4 (24) = 24/4 = 6
Je remarque que dans les 2 cas précédents, on a : A = a * b
1*5=5 et (-2)*(-3)=6
3) 1/4 ((a+b)²-(a-b)²)
= 1/4 ((a²+2ab+b²)-(a²-2ab+b²))
= 1/4 (a²-a² + b²-b² + 2ab + 2ab)
= 1/4 (4ab)
= (4ab)/4
= ab
