Question

What is the coefficient of the X^6Y^3 term in the expansion of (x + 2y)^9?

a) 84
b) 168
c) 336
d) 672

Answer 1

Using the binomial theorem, the coefficient of the X^6Y^3 term in the expansion of (x + 2y)^9 is calculated to be 672, making option d) the correct answer.

Step-by-step explanation:

The coefficient of the X^6Y^3 term in the expansion of (x + 2y)^9 can be found using the binomial theorem. The general term in a binomial expansion is given by:

T(n+1) = nCr * a^(n-r) * b^r

Where n is the power of the binomial, r is the term number, a and b are the terms in the binomial, and nCr is the combination of n things taken r at a time.

For the X^6Y^3 term, r will be 3 to have the Y^3 and hence the power of X will be 9 - 3 = 6. Using the formula:

9C3 * x^6 * (2y)^3 = 84 * x^6 * 8y^3 = 672 * x^6y^3

Therefore, the coefficient is 672, which corresponds to option d).