No problem! I can help you with that.
The binomial formula allows us to expand expressions of the form (a + b)^n, where a and b are numbers and n is a positive integer. The formula states that:
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n
In this case, our expression is (y + 2s)^25, where a = y, b = 2s, and n = 25.
To find the coefficient of the y^24 * s term, we are looking for the term in the expansion of (y + 2s)^25 that contains (y^24) * (2s^1).
The coefficient of this term can be determined using the binomial coefficient, which is given by the combination formula:
C(n, k) = n! / (k! * (n-k)!)
Where n is the total number of terms (25 in this case) and k is the power of the variable we are interested in (1 for the power of s and 24 for the power of y in our case).
So, the coefficient of the y^24 * s term can be calculated as:
C(25, 1) = 25! / (1! * (25-1)!) = 25
Therefore, the coefficient of the y^24 * s term in the expansion of (y + 2s)^25 is 25.