StudyGPT Just Leveled Up – Say Hello to Knowee! 🚀
Knowee
Questions
Features
Study Tools

Determine the coefficient, a, for the term ax5y7 of the binomial expansion of (2x+y)12.

Question

🧐 Not the exact question you are looking for?Go ask a question

Solution

The binomial expansion of (2x+y)^12 can be represented by the binomial theorem as follows:

(2x+y)^12 = Σ (from k=0 to 12) [12Ck * (2x)^(12-k) * (y)^k]

The term ax^5y^7 corresponds to the case where k=7 (because the power of y is 7). So, we substitute k=7 into the binomial theorem:

a = 12C7 * (2x)^(12-7) * (y)^7 a = 792 * (2x)^5 * y^7 a = 792 * 32x^5 * y^7 a = 25344x^5 * y^7

So, the coefficient a for the term ax^5y^7 of the binomial expansion of (2x+y)^12 is 25344.

This problem has been solved

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.