Mathematics - Binomial Theorem Question with Solution | TestHub

$(1-y{)}^m(1+y{)}^n=\left[1-{}^m{C}_{1}y+{}^m{C}_2{y}^2-\dots \right]\left[1+{}^n{C}_{1}y+{}^n{C}_2{y}^2+\dots \right]$ $=1+(n-m)+\left\{\frac{m(m-1)}{2}+\frac{n(n-1)}{2}-mn\right\}{y}^2+\dots .$. $\therefore a_1=n-m=10$ and $a_2=\frac{m^2+n-m-n-2mn}{2}=10$ So, $n-m=10$ and $(m-n{)}^2-(m+n)=20\Rightarrow m+n=80$ $$\therefore \mathrm{m}=35,\mathrm{n}=45$$