Q:

Complete the following statements in relation to the third term in the expansion of the binomial (2x+y^2)^5

Accepted Solution

A:
We want to expand (2x + y²)⁵.

From Pascal's Triangle (shown below), the coefficients of the expansion are
1,5,10,10,5,1.

n=0:                        1
n=1:                      1      1
n=2:                   1    2     1
n=3:                 1   3    3     1
n=4:               1   4   6    4     1
n=5:             1   5  10  10   5     1

Therefore the third term in the expansion is 
10*(2x)³*(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴

Alternatively, the third term is
₅C₃ (2x)³(y²)² = 10*(8x³)*(y⁴) = 80x³y⁴

Answer: 80x³y⁴