Question

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

a. 10C5⋅(5y)⁵⋅35
b. 10C6⋅(5y)⁴⋅36
c. 5⋅10C5⋅(y)⁵⋅35
d. 5⋅10C6⋅(y)⁴⋅36

Answer 1

The sixth term in the binomial expansion of (5y+3)¹⁰ is represented by 10C5·(5y)⁵·3⁵, corresponding to the formula for the (k+1)th term in the expansion.

"the correct option is approximately option A"

Step-by-step explanation:

The sixth term in the binomial expansion of (5y+3)¹⁰ is given by the general formula for the binomial theorem, which in simpler terms is written as:

T(k+1) = nCk · (first term)^(n-k) · (second term)^k

Where T(k+1) is the (k+1)th term, nCk represents the binomial coefficient, and n is the power of the expansion. To find the sixth term, we set k to 5, since the first term is T(1) when k=0.

So for the sixth term (k=5), we get:

T(6) = 10C5 · (5y)^(10-5) · 3^5

Therefore, the correct expression for the sixth term is:

10C5·(5y)⁵·3⁵

This matches one of the given options:

a. 10C5·(5y)⁵·3⁵