Given the expression (2x+3y^2)^5 , determine the total number of terms in its expansion:(K:1)

Question

BlackTom AI · Accepted Answer

To determine how many terms appear in the expansion of (2x + 3y^2)^5, consider the binomial expansion where each term takes the form (2x)^k (3y^2)^{5-k} for k = 0, 1, 2, 3, 4, 5. There are six possible values of k, corresponding to six terms in the expanded expression. Each term has distinct exponents: x^k y^{2(5-k)} yields exponents (x^0 y^10), (x^1 y^8), (x^2 y^6), (x^3 y^4), (x^4 y^2), and (x^5 y^0). Since no two terms share the same combination of exponents, none of the terms combine with another, so the total number of terms is 6. If one were to count the terms directly from the binomial formula, the same result emerges: a 5th-degree binomial expansion produces 5 + 1 = 6 terms. In short, the expansion yields six distinct terms, so the answer is 6.

Given the expression (2x+3y^2)^5 , determine the total number of terms in its expansion:(K:1)单项选择题

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