Final answer:
The coefficient of the term a9b2c5de2 in the product (a + b + c + d + e)²⁵ can be determined using the binomial theorem.
Step-by-step explanation:
The coefficient of the term a9b2c5de2 in the product (a + b + c + d + e)²⁵ can be determined using the binomial theorem. The binomial theorem states that for any power of a binomial, the coefficients of the terms can be calculated using the combinations formula, which is nCk. In this case, a has an exponent of 9, b has an exponent of 2, c has an exponent of 5, d has an exponent of 1, and e has an exponent of 2. So the coefficient of the term is 25C9 * 9C2 * 5C5 * 1C1 * 2C2.