Factorise
` 1- ( 2x- 3y ) ^(2)`

Answer

To factorise the expression \( 1 - (2x - 3y)^2 \), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ 1 - (2x - 3y)^2 \]

### Step 2: Recognize the difference of squares
We can recognize that this expression is in the form of \( a^2 - b^2 \), where:
- \( a = 1 \) (which is \( 1^2 \))
- \( b = (2x - 3y) \)

### Step 3: Apply the difference of squares formula
The difference of squares formula states that:
\[ a^2 - b^2 = (a - b)(a + b) \]
Applying this formula:
\[ 1 - (2x - 3y)^2 = (1 - (2x - 3y))(1 + (2x - 3y)) \]

### Step 4: Simplify the factors
Now we simplify the factors:
1. The first factor:
\[ 1 - (2x - 3y) = 1 - 2x + 3y \]
2. The second factor:
\[ 1 + (2x - 3y) = 1 + 2x - 3y \]

### Step 5: Write the final factorised form
Putting it all together, we have:
\[ 1 - (2x - 3y)^2 = (1 - 2x + 3y)(1 + 2x - 3y) \]

Thus, the final answer is:
\[ (1 - 2x + 3y)(1 + 2x - 3y) \]

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