Respuesta :
Answer:Term 11 = C(30, 11) * y^19 * (4^11) * x^11
Step-by-step explanation:
To find the 11th term in the expansion of the expression (y+4x)^30, we can use the binomial theorem. The binomial theorem allows us to expand a binomial raised to a power. In this case, we have (y+4x)^30. The binomial theorem states that the kth term in the expansion of (a+b)^n can be calculated using the formula: C(n, k) * a^(n-k) * b^k where C(n, k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items. It can be calculated using the formula: C(n, k) = n! / (k! * (n-k)!) In our case, a = y, b = 4x, and n = 30. We want to find the 11th term, so k = 11. Let's calculate the binomial coefficient C(30, 11): C(30, 11) = 30! / (11! * (30-11)!) Simplifying the expression, we have: C(30, 11) = 30! / (11! * 19!) Now, we can calculate the value of the 11th term: Term 11 = C(30, 11) * y^(30-11) * (4x)^11 Simplifying further: Term 11 = C(30, 11) * y^19 * (4^11) * x^11 This is the general formula for the 11th term in the expansion of (y+4x)^30. You can calculate the specific value by substituting the appropriate values for y and x. Remember, the binomial theorem is a powerful tool that allows us to expand binomial expressions raised to a power. By using the formula for the kth term, we can find specific terms in the expansion.
