Provide an appropriate response.In your own words, explain how to determine the binomial coefficient for x3y9 in the expansion of (x + y)12.

Question

What will be an ideal response?

Answer 1

The numerator of the binomial coefficient for x³y⁹ in the expansion of (x + y)¹² is a factorial of the exponent to which the binomial is raised (in this case, 12!). The denominator is a product of factorials: the power to which x is raised (in this case, 3!) and the degree of the binomial less the power to which x is raised (in this case, 9!). Thus, in this case, the binomial coefficient = . (Explanations will vary.)