Find the number of terms in the following expansions.
`( sqrt(3) + sqrt(5) )^(7) ( sqrt(3) - sqrt(5) )^(7)`

Answer

To find the number of terms in the expansion of \((\sqrt{3} + \sqrt{5})^7 (\sqrt{3} - \sqrt{5})^7\), we can follow these steps:

### Step 1: Recognize the Form
We start with the expression:
\[ (\sqrt{3} + \sqrt{5})^7 (\sqrt{3} - \sqrt{5})^7 \]
This can be rewritten using the identity \( (a + b)(a - b) = a^2 - b^2 \).

### Step 2: Apply the Identity
Let \( a = \sqrt{3} \) and \( b = \sqrt{5} \). Therefore, we can rewrite the expression as:
\[ ((\sqrt{3})^2 - (\sqrt{5})^2)^7 \]
Calculating \( (\sqrt{3})^2 \) and \( (\sqrt{5})^2 \):
\[ 3 - 5 = -2 \]
Thus, the expression simplifies to:
\[ (-2)^7 \]

### Step 3: Calculate the Result
Calculating \( (-2)^7 \):
\[ (-2)^7 = -128 \]

### Step 4: Determine the Number of Terms
The result of the expansion is a single term, \(-128\). Therefore, the number of terms in the expansion is:
\[ \text{Number of terms} = 1 \]

### Final Answer
The number of terms in the expansion is \( \boxed{1} \).

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