Apply the Binomial Theorem for expanding (x+y)^n using Pascal's Triangle or combinatorial reasoning.
Determine binomial-expansion degree and nonzero term count separately
Problem
Determine the index range, term count, total degree, and number of nonzero terms in the expansion of \((x~+~y)^6\).
Big Picture
What this problem is really about
Keep degree and term count as separate questions. The Binomial Theorem uses every integer index from zero through n, so count that range inclusively; meanwhile, each monomial’s two exponents add to n, which controls total degree. Finally, check whether coefficients vanish or exponent pairs repeat before declaring how many distinct nonzero terms remain.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
