Which expression represents the sixth term in the binomial expansion of (5y + 3)¹⁰?
¹⁰C₅(5y)⁵(3)^5
10C₆(5y)⁴(3)⁶
5(¹⁰C₅(y)⁵(3)⁵)
5(¹⁰C₆(y)⁴(3)⁶)

Solution:

Given, the expression is (5y + 3)¹⁰

We have to find the sixth term in the binomial expansion.

The general binomial expansion formula is given by

\((x+y)^{n}=^{n}C_{r}x^{(n-r)}y^{r}\)

Here, x = 5y, y = 3, n = 10, r = 6

\((5y+3)^{10}=^{10}C_{6}(5y)^{(10-6)}(3)^{6}\)

\((5y+3)^{10}=^{10}C_{6}(5y)^{(4)}(3)^{6}\)

Therefore, the sixth term of the given binomial expression is \((5y+3)^{10}= ^{10}C_{6}(5y)^{(4)}(3)^{6}\)

Which expression represents the sixth term in the binomial expansion of (5y + 3)¹⁰?

Summary:

The expression represents the sixth term in the binomial expansion of (5y + 3)¹⁰ is ¹⁰C₆(5y)⁴(3)⁶