Question

im2301_mvoa integrated math iii semester a_2439883 polynomial functions and equations which expression represents the sixth term in the binomial expansion of (5y + 3)^{10}? \\( 5_{10}c_6(y)^4(3)^6 \\) \\( _{10}c_6(5y)^4(3)^6 \\) \\( 5_{10}c_5(y)^5(3)^5 \\) \\( _{10}c_5(5y)^5(3)^5 \\)

Explanation:

Step1: Recall binomial theorem term formula

The $k$-th term (1-indexed) of $(a+b)^n$ is $\binom{n}{k-1}a^{n-(k-1)}b^{k-1}$.

Step2: Identify values for the formula

Here, $n=10$, $a=5y$, $b=3$, $k=6$. So $k-1=5$.

Step3: Substitute values into the formula

Term = $\binom{10}{5}(5y)^{10-5}(3)^5 = \binom{10}{5}(5y)^5(3)^5$.

Answer:

$\binom{10}{5}(5y)^5(3)^5$