Factorise
` 32a^(4) - 8a^(2)`

Answer

To factorise the expression \( 32a^4 - 8a^2 \), we can follow these steps:

### Step 1: Identify the common factor
First, we need to identify the common factor in both terms of the expression. The terms are \( 32a^4 \) and \( -8a^2 \).

The common factor here is \( 8a^2 \).

### Step 2: Factor out the common factor
Now, we can factor out \( 8a^2 \) from the expression:

\[ 32a^4 - 8a^2 = 8a^2(4a^2 - 1) \]

### Step 3: Recognize the difference of squares
Next, we notice that \( 4a^2 - 1 \) is a difference of squares. We can use the identity \( a^2 - b^2 = (a - b)(a + b) \) to factor this further. Here, \( a = 2a \) and \( b = 1 \).

### Step 4: Apply the difference of squares identity
Using the difference of squares identity, we can factor \( 4a^2 - 1 \):

\[ 4a^2 - 1 = (2a - 1)(2a + 1) \]

### Step 5: Combine the factors
Now, we can combine everything we have factored:

\[ 32a^4 - 8a^2 = 8a^2(2a - 1)(2a + 1) \]

### Final Answer
Thus, the fully factored form of the expression \( 32a^4 - 8a^2 \) is:

\[ 8a^2(2a - 1)(2a + 1) \]

---