Question

Calcule o valor da expressao 53^4 - 4.53^3.50 +6.53^2.50^2 -4.53.50^3 +50^4 (53 pontos !!!)

Answer 1

53^4 - 4 . 53^3 . 50 + 6 . 53^2 . 50^2 - 4 . 53 . 50^3 + 50^4
7890481 - 29775400 + 42135000 - 26500000 + 6250000
81

Answer 2

Binômio de Newton

Conforme Triângulo de Pascal

Termo n=4

x˄4 + 4.x˄3.a + 6.x˄2.a˄2 – 4.x.a˄3 + a˄4 = (x – a)˄4  

53˄4 + 4.53˄3 + 6.53˄2.50˄2 – 4.53.50˄3 + 50˄4

X = 53; a = 50  

Substituindo: (x – a)˄4 = (53 – 50)˄4 = 3˄4 = 3.3.3.3 = 81