Fractorise:
`4x ^(2) -9y^(2)`

Answer

To factorize the expression \( 4x^2 - 9y^2 \), we can follow these steps:

### Step 1: Identify the squares
We can rewrite \( 4x^2 \) and \( 9y^2 \) as perfect squares:
- \( 4x^2 = (2x)^2 \)
- \( 9y^2 = (3y)^2 \)

### Step 2: Recognize the difference of squares
The expression \( 4x^2 - 9y^2 \) can now be recognized as a difference of squares:
\[ (2x)^2 - (3y)^2 \]

### Step 3: Apply the difference of squares formula
The difference of squares can be factored using the formula:
\[ a^2 - b^2 = (a + b)(a - b) \]
In our case, \( a = 2x \) and \( b = 3y \).

### Step 4: Substitute \( a \) and \( b \) into the formula
Now we can substitute \( a \) and \( b \) into the formula:
\[ (2x + 3y)(2x - 3y) \]

### Final Answer
Thus, the factorization of \( 4x^2 - 9y^2 \) is:
\[ (2x + 3y)(2x - 3y) \]

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