Chapter 10 Counting Methods and Probability - 10.5 Find Probabilities of Independent and Dependent Events - 10.5 - Mixed Review - Page 723: 45

$$2187x^7+10206x^6+20412x^5+22680x^4+15120x^3+6048x^2+1344x+128$$

Using the binomial expansion theorem, we can expand the binomial without multiplying it out. Doing this, we find: $$2187x^7+10206x^6+20412x^5+22680x^4+15120x^3+6048x^2+1344x+128$$