Factorise :
`4a^(2) - 49b^(2) + 2a - 7b`

Answer

To factorise the expression \( 4a^2 - 49b^2 + 2a - 7b \), we can follow these steps:

### Step 1: Rearrange the expression
We start with the expression:
\[ 4a^2 - 49b^2 + 2a - 7b \]
We can rearrange it to group the terms:
\[ 4a^2 + 2a - 49b^2 - 7b \]

### Step 2: Factor out perfect squares
Notice that \( 4a^2 \) can be expressed as \( (2a)^2 \) and \( 49b^2 \) can be expressed as \( (7b)^2 \). Thus, we can rewrite the expression as:
\[ (2a)^2 - (7b)^2 + 2a - 7b \]

### Step 3: Recognize the difference of squares
The expression \( (2a)^2 - (7b)^2 \) is a difference of squares, which can be factored using the identity \( x^2 - y^2 = (x - y)(x + y) \):
\[ (2a - 7b)(2a + 7b) + 2a - 7b \]

### Step 4: Factor by grouping
Now we can factor out the common term \( (2a - 7b) \):
\[ (2a - 7b)(2a + 7b + 1) \]

### Final Answer
Thus, the factorised form of the expression \( 4a^2 - 49b^2 + 2a - 7b \) is:
\[ (2a - 7b)(2a + 7b + 1) \]