Man bezeichnet die Formel
(a+b)(a-b) = a2 – b2
als dritte binomische Formel. Die folgenden zwölf Beispiele demonstrieren ihre Verwendung:
(x-v)(x+v) = x2 – v2
(t+f)(t-f) = t2 – f2
(y-3)(y+3) = y2 – 32 = y2 – 9
(1+k)(1-k) = 12 – k2 = 1 – k2
(20-13y)(20+13y) = 202 – (13y)2 = 400 – 169y2
(5t-x)(5t+x) = (5t)2 – x2 = 25t2 – x2
(-3-30w)(-3+30w) = (-3)2 – (30w)2 = 9 – 900w2
(-8c-3)(-8c+3) = (-8c)2 – 32 = 64c2 – 9
(15x-13y)(15x+13y) = (15x)2 – (13y)2 = 225x2 – 169y2
(12a-7b)(12a+7b) = (12a)2 – (7b)2 = 144a2 – 49b2
(-5p+3q)(-5p-3q) = (-5p)2 – (3q)2 = 25p2 – 9q2
(-14u+3m)(-14u-3m) = (-14u)2 – (3m)2 = 196u2 – 9m2