Factorise by grouping method :
`16(a + b)^(2) - 4a - 4b`

Answer

To factorise the expression \( 16(a + b)^2 - 4a - 4b \) by grouping, we can follow these steps:

### Step 1: Rewrite the Expression
Start with the given expression:
\[ 16(a + b)^2 - 4a - 4b \]

### Step 2: Factor Out Common Terms
Notice that the last two terms, \(-4a\) and \(-4b\), can be factored by taking \(-4\) common:
\[ 16(a + b)^2 - 4(a + b) \]

### Step 3: Identify Common Factors
Now, we can see that both terms share a common factor of \((a + b)\):
\[ = (a + b)(16(a + b) - 4) \]

### Step 4: Simplify the Remaining Expression
Now simplify the expression inside the parentheses:
\[ = (a + b)(16(a + b) - 4) \]
This can be rewritten as:
\[ = (a + b)(16(a + b) - 4) \]

### Step 5: Factor Further if Possible
We can factor out the constant from the second term:
\[ = (a + b)(4(4(a + b) - 1)) \]

### Final Factorised Form
Thus, the final factorised form of the expression is:
\[ = 4(a + b)(4(a + b) - 1) \]