How do you solve this equation? Binomial expansion?

Question

Was some time ago I did this, what pops into my mind is binomial expansion/pascals triangle to find the coefficient infront of X^100 but I can't remember how, could someone show me? Equation

$$\sum_{j=0}^{50}{50\choose j}8^j=x^{100}$$

Answer 1

Observe that $$3^{100} = 9^{50} = (1+8)^{50} = \sum_{j=0}^{50} \binom{50}{j} 8^j.$$