If A be the sum of odd terms and B be the sum of even terms in the expansion of `(x+a)^(n) `, prove that `A^(2) -B^(2) = (x^(2) - a^(2)) ^(n)`

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^n , prove that (i) p^2 - Q^2 = (x^2 - a^2)^(n)

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

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^n , prove that (iii) 2(P^2 + Q^2 ) = (x+a)^(2n) + (x-a)^(2n) .

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 P^(2)-Q^(2)=(x^(2)-a^(2))^(n)

If P be the sum of odd terms and Q be the sum of even terms in the expansion of (x+a)^(n) , then (x+a)^(2n)+(x-a)^(2n) is (i) P^(2)-Q^(2) (ii) P^(2)+Q^(2) (iii) 2(P^(2)+Q^(2)) (iv) 4PQ

If the sum of odd terms and the sum of even terms in the expansion of (x+a)^n are p and q respectively then p^2+q^2=

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: (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)

Find the number of terms in the expansion of (1-2x+x^(2))^(n) .

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