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

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