The given expression is (2x + 1/x)^n. We need to find the constant term in the expansion of this expression.

To find the constant term, we can use the binomial theorem. According to the binomial theorem, the general term in the expansion of (a + b)^n is given by the formula:

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

Where T(r+1) is the (r+1)th term in the expansion, nCr represents the binomial coefficient, a is the first term (2x), b is the second term (1/x), and r is the index of the term.

Now, let's expand the given expression using the binomial theorem:

(2x + 1/x)^n = (nC0) * (2x)^(n-0) * (1/x)^0 + (nC1) * (2x)^(n-1) * (1/x)^1 + (nC2) * (2x)^(n-2) * (1/x)^2 + ...

Since we are interested in finding the constant term, we need to find the term where the exponent of x is 0 (x^0 = 1).

From the expansion, we can see that the exponent of x in each term is given by (n - r). So, for the constant term, we need to find the value of r such that (n - r) = 0.

Solving the equation, we get r = n.

So, the constant term in the expansion is given by:

T(n+1) = (nCn) * (2x)^(n-n) * (1/x)^n

Simplifying this expression, we get:

T(n+1) = (nCn) * 2^n

We are given that the sum of the binomial coefficients is equal to 256. Therefore, we can write:

(nC0) + (nC1) + (nC2) + ... + (nCn) = 256

Substituting the value of T(n+1) in this equation, we get:

T(n+1) = 2^n = 256

Taking logarithm base 2 on both sides, we get:

n = log2(256) = 8

Now, substituting the value of n in T(n+1), we get:

T(8+1) = (8C8) * 2^8 = 1 * 2^8 = 256

Therefore, the constant term in the expansion is 256, which corresponds to option A.

The constant term is its middle term