Expand Expression: Expand the expression (j+k)3 using the binomial theorem.The binomial theorem states that (a+b)n can be expanded as a sum of terms in the form of C(n,k)⋅a(n−k)⋅bk, where C(n,k) is the binomial coefficient.For (j+k)3, we have:(j+k)3=j3+3j2k+3jk2+k3
Binomial Theorem Explanation: Identify the term with the highest total degree of j and k in the expanded form.Looking at the expanded form, we see that the terms are j3, 3j2k, 3jk2, and k3.Each term has a total degree of 3 (since j3 has j to the power of 3, 3j2k has k1 and k to the power of k3 which adds up to 3, and so on).
Identify Highest Degree Term: Determine the degree of the polynomial. Since the highest total degree of any term in the expanded form of j+k)3is$3, the degree of the polynomial j+k)3is$3.