Question

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

Answer 1

coefficient = 80

The power of x = 3

The power of y = 4

Explanation:

did the test on plato/edmentum and got it right

Answer 2

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