Question

Find the middle term of the expansion of (x+y)^8 a40x^2y^2 b70x^2y^2

Answer 1

the middle term = 70x⁴y⁴

Explanation:

Given;

(x+y)⁸

This expression can be expanded as follows, using Paschal triangle;

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

At level 8, the middle coefficient is 70

Also the power of x and y will be equal in the middle term = A(xⁿ yⁿ)

A = 70 ,

n +n = 8

n = 4

Thus, the middle term = 70x⁴y⁴