Question

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

Answer 1

If n is even, then the expansion of $\left\{\right(x+a{)}^n+(x-a{)}^n\}$ has $(\frac{n}{2}+1)$ terms So, $(2+\sqrt{3x}{)}^{10}+(2-\sqrt{3x}{)}^{10}$ has 6 terms.