If`O`, be the sum of terms at odd position and `E` that of terms at the even position in the expansion `(x+a)^n`

If P be the sum of all odd terms and Q that of all even terms in the expansion of (x+a)^(n) , prove that

If P and Q are the sum of odd sum terms and the sum of even terms respectively in the expansion of (x +a)^n then prove that 4PQ = (x+a)^(2n) - (x - a)^(2n)

If P and Q are the sum of odd sum terms and the sum of even terms respectively in the expansion of (x +a)^n then prove that 4PQ = (x+a)^(2n) - (x - a)^(2n)

If o be the sum of odd terms and E that of even terms in the expansion of (x+a)^(n) prove that: O^(2)-E^(2)=(x^(2)-a^(2))^(n)( (i) 4OE=(x+a)^(2n)-(x-a)^(2n)( iii) 2(O^(2)+E^(2))=(x+a)^(2n)+(x-a)^(2n)

If o be the sum of odd terms and E that of even terms in the expansion of (x+a)^n prove that: (i) O^2-E^2=(x^2-a^2)^n (ii) 4O E=(x+a)^(2n)-(x-a)^(2n) (iii) 2(O^2+E^2)=(x+a)^(2n)+(x-a)^(2n)

If n is a positive integer, show that, in the expansion of (1+x)^(n) the sum of the coefficents of terms in the odd positions is equal to the sum of the cofficients of term in the even positions and each sum is equal to 2^(n-1) .

If A and B respectively denote the sum of the odd terms and sum of the even terms in the expansion of (x+y)^(n), then the value of (x^(2)-y^(2))^(n), is equal to

If A and B respectively denote the sum of the odd terms and sum of the even terms in the expansion of (x+y)^n , then the value of (x^2-y^2)^n , is equal to

If P and Q are the sum of odd terms and the sum of even terms respectively in the expansion of (x+a)^(n) then prove that 4PQ=(x+a)^(2n)-(x-a)^(2n)

If n is a positive integer, then the number of terms in the expansion of (x + a)^n is