Mathematics - Binomial Theorem Question with Solution | TestHub

From the given condition, replacing $a$ by a and $-ai$ respectively, we get $(x+ai{)}^n=\left(T_0-T_2+T_4-\dots \dots \right)+i\left(T_1-T_3+T_5-\dots .\right)$ ...(i) and $(x-ai{)}^n=\left(T_0-T_2+T_4-\dots \dots \right)-i\left(T_1-T_3+T_5-\dots \right)$...(ii) Multiplying (ii) and (i) we get required result i.e., $${\left(x^2+a^2\right)}^n={\left(T_0-T_2+T_4-\dots .\right)}^2+{\left(T_1-T_3+T_5-\dots \right)}^2$$