Write the number of terms in the expansion of

Question:

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

Solution:

Number of terms in the expansion $(x+y)^{n}+(x-y)^{n}$ where $n$ is even $=\left(\frac{n}{2}+1\right)$

Thus, we have:

Number of terms in the given expansion $=\left(\frac{10}{2}+1\right)=6$

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