which expression represents the sixth term in the binomial expansion of (5y + 3)^10?\n10c5(5y)^5(3)^5\n10c6(5…

which expression represents the sixth term in the binomial expansion of (5y + 3)^10?\n10c5(5y)^5(3)^5\n10c6(5y)^4(3)^6\n510c5(y)^5(3)^5\n510c6(y)^4(3)^6

which expression represents the sixth term in the binomial expansion of (5y + 3)^10?\n10c5(5y)^5(3)^5\n10c6(5y)^4(3)^6\n510c5(y)^5(3)^5\n510c6(y)^4(3)^6

Answer

Explanation:

Step1: Recall binomial - theorem formula

The general term in the binomial expansion of ((a + b)^n) is given by (T_{r + 1}={n}C{r}a^{n - r}b^{r}), where (n) is the power of the binomial, (r) is the term - number minus 1, (a) and (b) are the two terms of the binomial.

Step2: Identify the values of (n), (a), (b), and (r)

Here, (n = 10), (a = 5y), (b = 3). We want the sixth term, so (r+1 = 6), then (r = 5).

Step3: Substitute the values into the formula

(T_{6}={10}C{5}(5y)^{10 - 5}(3)^{5}={10}C{5}(5y)^{5}(3)^{5})

Answer:

A. ({10}C{5}(5y)^{5}(3)^{5})