Final answer:
The coefficient of y⁵ in the expression (3x+2y)⁸ is 56. Option a is correct.
Step-by-step explanation:
To find the coefficient of y⁵ in the expression (3x+2y)⁸, we can use the binomial theorem.
According to the binomial theorem, the coefficient of y⁵ in (3x+2y)⁸ is given by the formula:
(8 choose 5) * (3x)^(8-5) * (2y)^5
Simplifying this expression, we get:
(8 choose 5) * 3^(8-5) * (x^3) * 2^5 * y⁵
Using the formula for combinations, (8 choose 5) = 8! / (5! * (8-5)!), which simplifies to 56.
Therefore, the coefficient of y⁵ in the expression (3x+2y)⁸ is 56.
Therefore, Option a is correct.