In the expansion of `(x+a)^(n)`, the sum of even terms is E, the sum of even terms is E, the sum of odd terms is O, then `O^(2)-E^(2)` is equal to

Options

A. `(x +a)^(2n) + (x -a)^(2n)`
B. `(1)/(2) {(x +a)^(2n) + (x - a)^(2n)}`
C. `(1)/(2) {(x +a)^(2n) - (x - a)^(2n)}`
D. `(x + a)^(2n) - (x -a)^(2n)`

Answer

b

Explanation

We have ,
`(x +a)^(n) = O + E and (x -a)^(n) = =O - E`
`therefore O^(2) + E^(2) = (1)/(2) {(O+E)^(2) - (O-E)^(2)} = (1)/(2) {(x+a)^(2n) - (x -a)^(2n)}`.