Question

The number of non-zero terms in the expansion of $(1+3\sqrt{2x})^9 + (1-3\sqrt{2x})^9$ is

• A. 10
• B. 9
• C. 5
• D. 0

Answer 1

Answer: (C)

5

Answer 2

The expansion of $(1+3\sqrt{2x})^9 + (1-3\sqrt{2x})^9$ is of the form $(a+b)^n + (a-b)^n$. When these two binomial expansions are added, terms with odd powers of $b$ (i.e., $3\sqrt{2x}$) cancel out, and terms with even powers of $b$ are doubled.

Since $n=9$ (an odd number), the powers of $b$ that remain are $b^0, b^2, b^4, b^6, b^8$.

There are 5 such terms. Each of these terms will have a non-zero coefficient, resulting in 5 non-zero terms in the expansion.