Chapter 10 Counting Methods and Probability - 10.5 Find Probabilities of Independent and Dependent Events - 10.5 - Mixed Review - Page 723: 47

$$4096x^6+6144x^5y+3840x^4y^2+1280x^3y^3+240x^2y^4+24xy^5+y^6$$

Using the binomial expansion theorem, we can expand the binomial without multiplying it out. Doing this, we find: $$4096x^6+6144x^5y+3840x^4y^2+1280x^3y^3+240x^2y^4+24xy^5+y^6$$