if the sum of odd terms and the sum of even terms in (x+a)ⁿ are p and q respectively then p²+q²=

P^2-Q^2 can be written as (P+Q)(P-Q). P+Q is equal to (x+a)^n and P-Q is equal to nC0×x^n-nC1×x^(n-1)+nC2×x^(n-2)-… or (x-a)^n.

So P^2-Q^2=(x+a)^n×(x-a)^n=(x^2-a^2)^n