Factorise:
` (x-2) (x+2) +3`

Answer

To factorise the expression \( (x-2)(x+2) + 3 \), we will follow these steps:

### Step 1: Recognize the Difference of Squares
The expression \( (x-2)(x+2) \) can be recognized as a difference of squares. According to the difference of squares formula, \( a^2 - b^2 = (a-b)(a+b) \). Here, we can let \( a = x \) and \( b = 2 \).

### Step 2: Apply the Difference of Squares Formula
Using the formula, we can rewrite \( (x-2)(x+2) \) as:
\[ x^2 - 2^2 = x^2 - 4 \]

### Step 3: Substitute Back into the Expression
Now, substitute back into the original expression:
\[ x^2 - 4 + 3 \]

### Step 4: Simplify the Expression
Combine the constant terms:
\[ x^2 - 4 + 3 = x^2 - 1 \]

### Step 5: Recognize Another Difference of Squares
Now, we see that \( x^2 - 1 \) is also a difference of squares:
\[ x^2 - 1^2 = (x-1)(x+1) \]

### Final Answer
Thus, the factorised form of the expression \( (x-2)(x+2) + 3 \) is:
\[ (x-1)(x+1) \]

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