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(j+k)3(j+k)^3

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Q. (j+k)3(j+k)^3
  1. Expand Expression: Expand the expression (j+k)3(j+k)^3 using the binomial theorem.\newlineThe binomial theorem states that (a+b)n(a+b)^n can be expanded as a sum of terms in the form of C(n,k)a(nk)bkC(n, k) \cdot a^{(n-k)} \cdot b^k, where C(n,k)C(n, k) is the binomial coefficient.\newlineFor (j+k)3(j+k)^3, we have:\newline(j+k)3=j3+3j2k+3jk2+k3(j+k)^3 = j^3 + 3j^2k + 3jk^2 + k^3
  2. Binomial Theorem Explanation: Identify the term with the highest total degree of jj and kk in the expanded form.\newlineLooking at the expanded form, we see that the terms are j3j^3, 3j2k3j^2k, 3jk23jk^2, and k3k^3.\newlineEach term has a total degree of 33 (since j3j^3 has jj to the power of 33, 3j2k3j^2k has kk11 and kk to the power of kk33 which adds up to 33, and so on).
  3. 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)3 is$3j+k)^3\ is \$3, the degree of the polynomial j+k)3 is$3j+k)^3\ is \$3.

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