Factorise :
`(2a + b)^(2) - 6a - 3b - 4`

Answer

To factorise the expression \( (2a + b)^2 - 6a - 3b - 4 \), we will follow these steps:

### Step 1: Rewrite the Expression
We start with the expression:
\[ (2a + b)^2 - 6a - 3b - 4 \]

### Step 2: Group the Terms
We can group the terms involving \( a \) and \( b \):
\[ (2a + b)^2 - (6a + 3b + 4) \]

### Step 3: Factor Out Common Terms
Notice that from the terms \( -6a - 3b \), we can factor out \(-3\):
\[ (2a + b)^2 - 3(2a + b) - 4 \]

### Step 4: Substitute for Simplicity
Let \( x = 2a + b \). Then, we can rewrite the expression as:
\[ x^2 - 3x - 4 \]

### Step 5: Factor the Quadratic Expression
Now we need to factor the quadratic \( x^2 - 3x - 4 \). We look for two numbers that multiply to \(-4\) (the constant term) and add up to \(-3\) (the coefficient of \( x \)). The numbers \(-4\) and \(1\) satisfy this:
\[ x^2 - 4x + x - 4 = (x - 4)(x + 1) \]

### Step 6: Substitute Back
Now we substitute back \( x = 2a + b \):
\[ (2a + b - 4)(2a + b + 1) \]

### Final Answer
Thus, the factorised form of the expression \( (2a + b)^2 - 6a - 3b - 4 \) is:
\[ (2a + b - 4)(2a + b + 1) \]

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