Factorise
` 98 ( a+b)^(2) - 2`

Answer

To factorise the expression \( 98 (a + b)^2 - 2 \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 98 (a + b)^2 - 2 \]

### Step 2: Divide by 2
To simplify the expression, we can divide the entire expression by 2:
\[ \frac{98 (a + b)^2 - 2}{2} = 49 (a + b)^2 - 1 \]

### Step 3: Recognize the difference of squares
Now we have:
\[ 49 (a + b)^2 - 1 \]
This expression is in the form of a difference of squares, which can be expressed as \( X^2 - Y^2 \) where \( X = 7(a + b) \) and \( Y = 1 \).

### Step 4: Apply the difference of squares formula
Using the difference of squares formula \( X^2 - Y^2 = (X - Y)(X + Y) \), we can factor the expression:
\[ (7(a + b) - 1)(7(a + b) + 1) \]

### Step 5: Write the final factorized form
Thus, the factorized form of the original expression \( 98 (a + b)^2 - 2 \) is:
\[ (7(a + b) - 1)(7(a + b) + 1) \]

### Summary
The final factorized expression is:
\[ (7(a + b) - 1)(7(a + b) + 1) \]

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