Factorise :
`5a^(2) - b^(2) - 4ab + 7a - 7b`

Answer

To factorise the expression \(5a^2 - b^2 - 4ab + 7a - 7b\), we will follow these steps:

### Step 1: Rearrange and Group Terms
We start with the expression:
\[ 5a^2 - b^2 - 4ab + 7a - 7b \]
We can rearrange it to group similar terms:
\[ (5a^2 - 4ab - b^2) + (7a - 7b) \]

### Step 2: Factor the First Group
Now, let's focus on the first group \(5a^2 - 4ab - b^2\). We can rewrite \(5a^2\) as \(4a^2 + a^2\):
\[ (4a^2 + a^2 - 4ab - b^2) \]
Now, we can group \(4a^2 - 4ab\) and \(a^2 - b^2\):
\[ 4a(a - b) + (a^2 - b^2) \]

### Step 3: Apply the Difference of Squares
The expression \(a^2 - b^2\) can be factored using the difference of squares:
\[ a^2 - b^2 = (a + b)(a - b) \]
Thus, we have:
\[ 4a(a - b) + (a + b)(a - b) \]

### Step 4: Factor out the Common Term
Now we can factor out the common term \((a - b)\):
\[ (a - b)(4a + (a + b)) \]
This simplifies to:
\[ (a - b)(5a + b) \]

### Step 5: Factor the Remaining Terms
We still have the second group \(7a - 7b\):
\[ 7(a - b) \]
Now we can combine everything:
\[ (a - b)(5a + b) + 7(a - b) \]

### Step 6: Final Factorization
We can factor out \((a - b)\) from the entire expression:
\[ (a - b)((5a + b) + 7) \]
This simplifies to:
\[ (a - b)(5a + b + 7) \]

### Final Answer
Thus, the factorized form of the expression \(5a^2 - b^2 - 4ab + 7a - 7b\) is:
\[ \boxed{(a - b)(5a + b + 7)} \]