How do you find the 5th term in the expansion of the binomial (5a+6b)^5?

Oct 14, 2017

$32400 a {b}^{4}$

Explanation:

The fifth term descending a:

${5}^{1} \left(5 C 4\right) {a}^{1} {6}^{4} {b}^{4} = 5 \cdot 5 \cdot 1296 {a}^{1} {b}^{5} = 32400 a {b}^{4}$

Oct 18, 2017

$32400 a {b}^{4}$

Explanation:

The expansion will have six terms starting with ${a}^{5}$ and ending with ${b}^{5}$
Fifth term will be $5 C \left(5 - 1\right) \cdot {a}^{5 - 4} \cdot {b}^{4}$

Given a as (5a) & b as (6b)

We also know $5 C 4 = 5 C 1 = 5$.

Substituting in the 5^th term, we get

$= 5 \cdot \left(5 a\right) \cdot {\left(6 b\right)}^{4} = 32400 \cdot a \cdot {b}^{4}$