Question

Write the number of terms in the expansion of ${\left(2+\sqrt{3}x\right)}^{10}+{\left(2-\sqrt{3}x\right)}^{10}$.

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{expansion}(x+y{)}^n+(x-y{)}^n\mathrm{where}n\mathrm{is}\mathrm{even}=\left(\frac{n}{2}+1\right) \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Number}\mathrm{of}\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{expansion}=\left(\frac{10}{2}+1\right)=6 \end{gathered}$$