Factorise :
`50a^(3) - 2a`

Answer

To factorise the expression \(50a^3 - 2a\), we can follow these steps:

### Step 1: Identify the common factor
First, we look for common factors in both terms of the expression \(50a^3\) and \(-2a\). The common factor here is \(2a\).

### Step 2: Factor out the common factor
We can factor out \(2a\) from the expression:
\[ 50a^3 - 2a = 2a(25a^2 - 1) \]

### Step 3: Recognize the difference of squares
Now, we notice that \(25a^2 - 1\) is a difference of squares. We can rewrite it using the identity \(a^2 - b^2 = (a + b)(a - b)\).

Here, we can let:
- \(a = 5a\)
- \(b = 1\)

### Step 4: Apply the difference of squares identity
Using the difference of squares identity, we can factor \(25a^2 - 1\):
\[ 25a^2 - 1 = (5a + 1)(5a - 1) \]

### Step 5: Combine the factors
Now we can combine this with the factor we took out earlier:
\[ 50a^3 - 2a = 2a(25a^2 - 1) = 2a(5a + 1)(5a - 1) \]

### Final Answer
Thus, the fully factorised form of \(50a^3 - 2a\) is:
\[ \boxed{2a(5a + 1)(5a - 1)} \]